Tootfinder

Why the Eagles still don't have their Super Bowl rings, plus the top 25 moments of the past 25 years

https://www.cbssports.com/nfl/news/why-the

Almost Noetherian rings and modules
Xiaolei Zhang
https://arxiv.org/abs/2509.05996 https://arxiv.org/pdf/2509.05996…

Almost Noetherian rings and modules
In this paper, we investigate the notions of almost Noetherian rings and modules. In details, we give the Cohen type theorem, Eakin-Nagata type theorem, Kaplansky type Theorem and Hilbert basis theorem and some other rings constructions for almost Noetherian rings. In particular, we resolve a question proposed in [8].

Weakly Strongly 2-Nil-Clean Rings
Peter Danchev, Mina Doostalizadeh, Ahmad Moussavi
https://arxiv.org/abs/2509.05673 https://arxiv.org/pdf/2509.05673

Weakly Strongly 2-Nil-Clean Rings
In this paper, we introduce and explore in-depth the notion of {\it weakly strongly 2-nil-clean rings} as a common non-trivial generalization of both strongly 2-nil-clean rings and strongly weakly nil-clean rings as defined and studied by Chen-Sheibani in the J. Algebra \& Appl. (2017). We, specifically, succeeded to prove that any weakly strongly 2-nil-clean ring is strongly $π$-regular and, concretely, it decomposes as the direct product of a strongly 2-nil-clean ring and a ring of the type …

$\delta$-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Shinnosuke Ishiro, Kazuma Shimomoto
https://arxiv.org/abs/2509.06527 https://arxiv.org/…

$δ$-rings, perfectoid towers, and lim Cohen-Macaulay sequences
The aim of this article is to study basic structures and interrelations of $δ$-rings, perfectoid towers, and lim Cohen-Macaulay sequences over Noetherian rings in positive or mixed characteristic. Then we discuss some methods for constructing perfectoid towers, dealing with $p$-torsion free and $p$-torsion cases, respectively. Some interesting examples arise as quotients by monomial or binomial ideals or determinantal rings. We also explain a geometric method with a view toward constructing ri…

Rings on quotient divisible abelian groups
Kompantseva E., Nguyen T. Q. T
https://arxiv.org/abs/2509.05572 https://arxiv.org/pdf/2509.05572

Rings on quotient divisible abelian groups
The paper is devoted to the study of absolute ideals of groups in the class $\mathcal{QD}1$, which consists of all quotient divisible abelian groups of torsion-free rank 1. A ring is called an $AI$-ring (respectively, an $RF$-ring) if it has no ideals except absolute ideals (respectively, fully invariant subgroups) of its additive group. An abelian group is called an $RAI$-group (respectively, an $RFI$-group) if there exists at least one $AI$-ring (respectively, $FI$-ring) on it. If every absol…

Aharonov-Bohm interference from coherent spin-polarized edge transport in Fe(Te,Se) superconducting rings
Mohammad Javadi Balakan, Shiva Heidari, Genda Gu, Qiang Li, Kenji Watanabe, Takashi Taniguchi, Ji Ung Lee
https://arxiv.org/abs/2508.05030

Aharonov-Bohm interference from coherent spin-polarized edge transport in Fe(Te,Se) superconducting rings
We report the coexistence of Aharonov-Bohm and Little-Parks oscillations in mesoscopic Fe(Te,Se) rings. The magnetoresistance shows two distinct periodicities: an $h/e$ component from ballistic edge interference and an $h/2e$ component from fluxoid quantization of Cooper pairs. Aharonov-Bohm oscillations persist deep into the superconducting phase, exhibit current-field symmetry, and follow a temperature dependence captured by a helical Luttinger liquid model, consistent with edge states in a t…

On the Casimir number and formal codegree of Haagerup-Izumi fusion rings
Ying Zheng, Jiacheng Bao, Zhiqiang Yu
https://arxiv.org/abs/2509.06320 https://arx…

On the Casimir number and formal codegree of Haagerup-Izumi fusion rings
For any cyclic group $\mathbb{Z}_n$, we first determine the Casimir number and determinant of the Haagerup-Izumi fusion ring $\mathcal{HI}_{\mathbb{Z}_n}$, it turns out that they do not share the same set of prime factors. Then we show that all finite-dimensional irreducible representations of $\mathcal{HI}_{\mathbb{Z}_n}$ are defined over certain cyclotomic fields. As a direct result, we obtain the formal codegrees of $\mathcal{HI}_{\mathbb{Z}_n}$, which satisfy the pseudo-unitary inequality.

The mantra of "If you don't have time to do it right, what makes you think you have time to do it twice?" rings true, it *sounds* right.
But the whole point of agility is to see a third option:
If you don't have time to do it (the complete thing) right, maybe you have time to do part of it right, show the value in that, and then do the next part of it right.
I enjoy doing a good job as much as the next craftsman, but we also can't hold customer outcome…

On universal deformation rings and stable homogeneous tubes
Jhony F. Caranguay-Mainguez, Pedro Rizzo, Jose A. Velez-Marulanda
https://arxiv.org/abs/2507.03693

On universal deformation rings and stable homogeneous tubes
Let $\mathbf{k}$ be a field of any characteristic and let $Λ$ be a finite dimensional $\mathbf{k}$-algebra. We prove that if $V$ is a finite dimensional right $Λ$-module that lies in the mouth of a stable homogeneous tube $\mathfrak{T}$ of the Auslander-Reiten quiver $Λ$ with $\underline{\mathrm{End}}_Λ(V)$ a division ring, then $V$ has a versal deformation ring $R(Λ,V)$ isomorphic to $\mathbf{k}[\![t]\!]$. As consequence we obtain that if $\mathbf{k}$ is algebraically closed, $Λ$ is a sy…

Rings as unions of proper ideals
Malcolm Hoong Wai Chen
https://arxiv.org/abs/2508.05455 https://arxiv.org/pdf/2508.05455

Rings as unions of proper ideals
In this note, we define and investigate $\textit{ideal covering numbers}$ of associative rings (not assumed to be commutative or unital): three invariants defined as the minimal number of proper left, right, or two-sided ideals whose union equals the ring. For every prime $p$, we construct four infinite families of rings without identity that attain the sharp lower bound $p + 1$ for ideal covering numbers, each exhibiting distinct behavior with respect to left, right, and two-sided ideal coveri…

Bounds and MacWilliams Identities for codes over Artinian rings
Eduardo Camps-Moreno, Carlos Espinosa-Vald\'ez, Hiram H. L\'opez, Luis N\'u\~nez-Betancourt, Yuriko Pitones
https://arxiv.org/abs/2509.05850

Bounds and MacWilliams Identities for codes over Artinian rings
This work develops new foundations for the theory of linear codes over local Artinian commutative rings. We use algebraic invariants such as the socle, type, length, and minimal number of generators to measure the size of codes. We prove a relation between the type of a code and the free rank of its dual over Frobenius rings, extending previous results for chain rings. We also provide new upper bounds for the Hamming distance in terms of the length and type of a code and and conditions under wh…

Coherent and ideal actions in ideally exact categories
Manuel Mancini, Giuseppe Metere, Federica Piazza
https://arxiv.org/abs/2507.06124 https://

Coherent and ideal actions in ideally exact categories
In the context of ideally exact categories, we introduce the notions of internal coherent action and internal ideal action that generalize different aspects of unital actions of rings and algebras. We prove that every ideal action is coherent, and that the converse statement holds in some relevant ideally exact contexts. Furthermore, a connection with G. Janelidze's notion of semidirect product in ideally exact categories is analyzed.

Andre-Quillen (co)homology and Equivariant Stable Homotopy Theory
Ethan Leeman
https://arxiv.org/abs/2507.06099 https://arxiv.org/pdf…

Andre-Quillen (co)homology and Equivariant Stable Homotopy Theory
André and Quillen introduced a (co)homology theory for augmented commutative rings. Strickland initially proposed some issues with the analogue of the abelianization functor in the equivariant setting. These were resolved by Hill who further gave the notion of a genuine derivation and a module of Kähler differentials. We build on this endeavor by expanding to incomplete Tambara functors, introducing the cotangent complex and its various properties, and producing an analogue of the fundamental…

Replaced article(s) found for math.CO. https://arxiv.org/list/math.CO/new
[2/2]:
- On Modular Invariants of Truncated Polynomial Rings in low ranks
Le Minh Ha, Nguyen Dang Ho Hai, Nguyen Van Nghia

Residues and Gorenstein Contractions of Genus One Curves
Adrian Neff, Jonathan Wise
https://arxiv.org/abs/2507.05326 https://arxiv.or…

Residues and Gorenstein Contractions of Genus One Curves
Let $C$ be a genus one nodal curve over a local artinian base and let $E$ be a proper subcurve of genus one. We define residues for curves over local artinian rings, then define generalized residues with values in line bundles over the local artinian ring that arise from tropical data on the curve. We then use these residues to construct a contraction of $C$ that collapses $E$ to a Gorenstein genus one singularity.

Watching The Lord Of The Rings ext editions.
Ugh it’s just too much. But thankful on the last (4.5 hours). Then the Hobbot ones I guess.
Wife’s first time and she basically knew nothing of them.

Why the Eagles still haven't received their Super Bowl rings with training camp almost here

https://www.cbssports.com/nfl/news/why-the

A Non-leveled and Reliable Approximate FHE Framework through Binarized Polynomial Rings
Baigang Chen, Dongfang Zhao
https://arxiv.org/abs/2508.02943 https://

A Non-leveled and Reliable Approximate FHE Framework through Binarized Polynomial Rings
Homomorphic encryption (HE) enables secure computation on encrypted data, safeguarding user privacy in domains such as cloud computing, healthcare, and finance. Among fully homomorphic encryption (FHE) schemes, CKKS is notable for supporting approximate arithmetic over complex numbers, a key requirement for machine-learning and numerical workloads. However, CKKS incurs rapid noise growth, complex parameter tuning, and relies on costly modulus switching. We propose a binary variant of CKKS that …

Aye, I could do that.
👇
#Galway

Periodicity of ideals of minors over artinian stretched Gorenstein rings
Trung Chau
https://arxiv.org/abs/2507.05225 https://arxiv.or…

Periodicity of ideals of minors over artinian stretched Gorenstein rings
We prove that over artinian stretched Gorenstein rings, the ideals of minors of a minimal free resolution of any finitely generated module are eventually 2-periodic. This is an analog of results obtained over complete intersections and Golod rings proved by Brown, Dao, and Sridhar.

Alpha-, Beta-, and Gamma-TODD-G: Novel 2D Planar Carbon Allotropes
Kleuton A. L. Lima, Jose A. S. Laranjeira, Alysson M. A. Silva, Bill. D. Aparicio-Huacarpuma, Fabr\'icio M. Vasconcelos, Julio R. Sambrano, Douglas S. Galv\~ao, Luiz A. Ribeiro Junior
https://arxiv.org/abs/2508.05013

Alpha-, Beta-, and Gamma-TODD-G: Novel 2D Planar Carbon Allotropes
We present a comprehensive first-principles investigation of three novel two-dimensional carbon allotropes: alpha-, beta-, and gamma-TODD-Graphene (TODD-G), composed of 3-8-12-16, 3-8-12-16, and 3-4-8-12 interconnected carbon rings with sp/sp2 hybridization, respectively. Structural optimization, phonon spectra, and ab initio molecular dynamics simulations confirm their thermal and dynamical stability. All phases exhibit metallic electronic behavior, with distinct Dirac-like features and tilted…

LCD and self-orthogonal twisted group codes over finite commutative chain rings
Samir Assuena, Andr\'e Luiz Martins Pereira
https://arxiv.org/abs/2507.04013

LCD and self-orthogonal twisted group codes over finite commutative chain rings
In this paper, we shall study k-Galois LCD constacyclic group codes over finite commutative chain rings with identity. In particular, we shall characterize Galois LCD constacyclic codes over finite commutative chain ring with identity in terms of its idempotent generators and the classical involution using the twisted group ring structures and find some good LCD codes.

Alg\`ebre lin\'eaire
Alexis Marin
https://arxiv.org/abs/2508.04712 https://arxiv.org/pdf/2508.04712

Algèbre linéaire
After the language of module and theirs morphisms, this short course presents matricial calculus and determinants in a commutative ring as appliction of ``remarquable identities'' in the ring of polynomials with integer coefficients with variable coefficients and second member of the ``general Gauss method'' requiring the factoriality of such polynomial rings, here obtained by a modification of Zermolo's proof of the factoriality of the integers. As third part, using the, today almost forgotten…

Sober topologies on a set
Xiangrui Li, Qingguo Li, Dongsheng Zhao
https://arxiv.org/abs/2508.05419 https://arxiv.org/pdf/2508.05419

Sober topologies on a set
The collection of all topologies on a set X forms a complete lattice with respect to the inclusion order, which have been investigated by many researchers. Sobriety is one of the core and extensively studied properties in non-Hausdorff topology. This property plays a crucial role in characterizing the spectral spaces of commutative rings and topological spaces determined by their lattices of open sets. In this paper, we investigate the statute of sober topologies in the complete lattice of all …

On the inextensibility assumption in the stability of elastic rings: overhaul of a traditional paradigm
Federico Guarracino, Ida Mascolo
https://arxiv.org/abs/2509.02738 https:/…

On the inextensibility assumption in the stability of elastic rings: overhaul of a traditional paradigm
One of the oldest and most common structural engineering issues is the elastic buckling of circular rings under external pressure, which has a fundamental importance in a number of applications in general mechanics, engineering and bio-physics, just to name a few. Levy is considered to have provided the first significant solution to this problem in 1884, and most stability text-books make reference to this original solution, which is based on the Euler-Bernoulli beam model. Following this incip…

Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator
Kevin zu M\"unster, Florian Gebhard, Satoshi Ejima, Holger Fehske
https://arxiv.org/abs/2507.03125

Dynamical correlation functions for the one-dimensional Bose-Hubbard insulator
We calculate the dynamical current and kinetic-energy correlation functions for the first Mott lobe of the one-dimensional Bose-Hubbard model. We employ the strong-coupling expansion up to sixth order in $x=t/U$, and the dynamical density-matrix renormalization group method on rings with 64 sites. The correlation functions are finite above the single-particle gap with a square-root onset, as is also found from field theory close to the Mott transition. The correlation functions display a featur…

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma
Torben C. Frost
https://arxiv.org/abs/2508.00624 https://

Gravitational Lensing in the Schwarzschild Spacetime: Photon Rings in Vacuum and in the Presence of a Plasma
Astrophysical black holes are usually surrounded by an accretion disk. At least parts of these accretion disks consist of a plasma in which light rays with different energies are dispersed. However, we usually do not know the exact configurations of these plasmas. In this paper we will now use the example of a Schwarzschild black hole embedded in an inhomogeneous pressureless and nonmagnetised plasma to investigate how the structural changes of the photon rings can help us to determine the prop…

A parametrization of $3$-class groups of quadratic rings over Dedekind domains
Eliot Hodges, Ashvin A. Swaminathan
https://arxiv.org/abs/2509.01722 https://

A parametrization of $3$-class groups of quadratic rings over Dedekind domains
Let $R$ be a Dedekind domain with field of fractions $K$ and $\operatorname{char}(R)\neq3$. In this paper, we generalize Bhargava's parametrization of $3$-torsion ideal classes by binary cubic forms to work over $R$. Specifically, we construct arithmetic subgroups of $\operatorname{GL}_2(K)$ whose actions on certain lattices of binary cubic forms over $K$ parametrize $3$-torsion ideal classes in class groups of quadratic rings over $R$.

Frobenius and Verschiebung for $K$-theory of endomorphisms
Sanjana Agarwal, Jonathan Campbell, Diego Manco, Kate Ponto, Zhonghui Sun
https://arxiv.org/abs/2507.05956

Frobenius and Verschiebung for $K$-theory of endomorphisms
We show that the Frobenius and Verschiebung maps that are fundamental to Witt vectors lift to the reduced K-theory of endomorphisms. In particular, we define Frobenius and Verschiebung maps for the reduced K-theory of twisted endomorphisms of modules over non commutative rings and show they have the expected behavior after applying the iterated trace map

The F-pure threshold versus the a-invariant for standard graded rings
Suchitra Pande
https://arxiv.org/abs/2508.04940 https://arxiv.org/pdf/2508.04940

The F-pure threshold versus the a-invariant for standard graded rings
Hirose, Watanabe and Yoshida conjectured a criterion for a standard graded strongly $F$-regular ring to be Gorenstein in terms of the $F$-pure threshold. We complete the proof of this conjecture. We also prove natural extensions of the conjecture to section rings of normal, $F$-split projective varieties with respect to globally generated ample divisors. Our proof exploits the geometry of the Proj of the graded ring.

Jet-Driven Formation of Bipolar Rings in Planetary Nebulae: Numerical Simulations Inspired by NGC 1514
Muhammad Akashi (Technion, Israel), Ealeal Bear (Technion, Israel), Noam Soker (Technion, Israel)
https://arxiv.org/abs/2507.23670

Jet-Driven Formation of Bipolar Rings in Planetary Nebulae: Numerical Simulations Inspired by NGC 1514
We conduct three-dimensional hydrodynamical simulations of jets launched into a dense shell, reproducing two rings in a bipolar structure that resemble the two dusty rings of the planetary nebula (PN) NGC 1514. The scenario we simulate assumes that a strong binary interaction enhanced the mass loss rate from the asymptotic giant branch (AGB) stellar progenitor of NGC 1514, and shortly thereafter, the main-sequence companion accreted mass from the AGB star, launching a pair of jets. We find that…

The nine rings of the galaxy LEDA 1313424
Pierre Sikivie, Yuxin Zhao
https://arxiv.org/abs/2508.19421 https://arxiv.org/pdf/2508.19421

The nine rings of the galaxy LEDA 1313424
The galaxy LEDA 1313424 has recently been discovered to have nine rings [1]. The authors of the discovery paper interpret the rings to be the result of the passing of a smaller galaxy through the center of the LEDA galaxy 56 Myr ago. We point out several difficulties with this interpretation and propose instead that the rings of LEDA are the imprint upon baryonic matter of caustic rings of dark matter. Caustic rings of dark matter, with the pattern of radii observed in the LEDA galaxy, form if …

Construction of Bases in Modules over Laurent Polynomial Rings and Applications to Box Spline Prewavelets
Oleg Davydov, Anatolii Tushev
https://arxiv.org/abs/2508.01399 https://…

Construction of Bases in Modules over Laurent Polynomial Rings and Applications to Box Spline Prewavelets
We suggest a new method of basis construction for the kernel of a linear form on the Laurent polynomial module related to multivariate wavelets, and demonstrate its applications to box spline prewavelets, leading to small mask supports for $C^1$ cubic and $C^2$ quartic box splines in two variables, outperforming previously known constructions, and to trivariate piecewise linear prewavelets with at most 23 nozero mask coefficients.

On the formation of multiple dust-trapping rings in the inner Solar system
E. Lega, A. Morbidelli, F. Masset, W. B\'ethune
https://arxiv.org/abs/2508.02410 https://

On the formation of multiple dust-trapping rings in the inner Solar system
Isotopic properties of meteorites provide evidence that multiple dust trap or pressure bumps had to form and persist in the inner Solar System on a timescale of millions of years. The formation of a pressure bump at the outer edge of the gap opened by Jupiter blocks particles drifting from the outer to the inner disk. This is not enough to preserve dust in the inner disk. However, in low viscosity disks, under specific condition on the gas cooling time, massive planets can also open secondary g…

Of all the brain’s mysteries, few are so profound as why I awoke today at 0530 with a craving for a small bag of Burger Rings.

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Rings whose indecomposable modules are pure-projective or pure-injective
Fran\c{c}ois Couchot (LMNO)

Computing in complete local equicharacteristic Noetherian rings via topological rewriting on commutative formal power series
Adya Musson-Leymarie
https://arxiv.org/abs/2507.04045 …

Computing in complete local equicharacteristic Noetherian rings via topological rewriting on commutative formal power series
In commutative algebra, the theory of Gröbner bases enables one to compute in any finitely generated algebra over a given computable field. For non-finitely generated algebras however, other methods have to be pursued. For instance, it follows from the Cohen structure theorem that standard bases of formal power series ideals offer a similar prospect but for complete local equicharacteristic rings whose residue field is computable. Using the language of rewriting theory, one can characterise Gr…

On the Chow Rings of the Moduli Spaces $\mathcal{M}_{5,8}$ and $\mathcal{M}_{5,9}$
Yuhan Liu
https://arxiv.org/abs/2509.02950 https://arxiv.org/pdf/2509.02…

On the Chow Rings of the Moduli Spaces $\mathcal{M}_{5,8}$ and $\mathcal{M}_{5,9}$
In this paper we prove that the rational Chow rings of $\mathcal{M}_{5,8}$ and $\mathcal{M}_{5,9}$ are tautological, and that these moduli spaces have the Chow Künneth generation Property.

Proximal and Descriptive Topological Rings: Structure and Properties
Maram Almahariq
https://arxiv.org/abs/2509.01466 https://arxiv.org/pdf/2509.01466

Proximal and Descriptive Topological Rings: Structure and Properties
The set of open subsets in a proximity space (X,ζ) forms a topological system that enables the definition of proximal and descriptive topological groups. This framework naturally extends to proximal and descriptive topological rings as well. In this study, I review fundamental properties and related results, with particular emphasis on the definition of proximal and descriptive fields. In addition, I examine the behavior of closed sets in proximal and descriptive topological rings.

Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings
John Guaschi (LMNO, UNICAEN, CNRS, NU), Daniel Juan-Pineda (CCM)
https://arxiv.org/abs/2509.02195

Braid groups of the projective plane, mapping class groups of non-orientable surfaces and algebraic K-theory of their group rings
We describe the lower algebraic $K$-theory of the integral group ring of both the pure and full braid groups of the real projective plane $\mathbb{R}P^2$ with $3$ strings, as well as that of the integral group ring of the mapping class group of $\mathbb{R}P^2$ with $3$ marked points. In addition, we give a general formula for the algebraic $K$-theory groups of the group ring of the mapping class group of non-orientable surfaces with k marked points, where $k \geq 3$.

Lagrange-like interpolation in unitary rings, Boolean algebras and Boolean posets
Ivan Chajda, Helmut L\"anger
https://arxiv.org/abs/2508.04836 https://

Lagrange-like interpolation in unitary rings, Boolean algebras and Boolean posets
It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is possible if one considers a unitary ring or a Boolean algebra instead of a field. We get a positive answer to this question provided the similarity type of the algebra in question is enriched with one more unary operation, the so-called Baaz delta. We get an explicit construction of this interpolation polynomial in both…

BKA warnt vor gewaltverherrlichenden Online-Gruppen für Jugendliche
Von Hamburg aus soll der mutmaßliche Kopf eines Rings von Pädokriminellen ein Kind zum Suizid gedrängt haben. Das BKA warnt vor ähnlichen Gruppen im Netz.

Burnside rings for racks and quandles
Nadia Mazza, Markus Szymik
https://arxiv.org/abs/2507.01425 https://arxiv.org/pdf/2507.01425

Burnside rings for racks and quandles
We restructure and advance the classification theory of finite racks and quandles by employing powerful methods from transformation groups and representation theory, especially Burnside rings. These rings serve as universal receptacles for those invariants of racks and quandles that are additive with respect to decompositions. We present several fundamental results regarding their structure, including additive bases and multiplicative generators. We also develop a theory of marks, which is anal…

Exact treatment of rotation-induced modifications in two-dimensional quantum rings
Carlos Magno O. Pereira, Frankbelson dos S. Azevedo, Edilberto O. Silva
https://arxiv.org/abs/2506.23300

Exact treatment of rotation-induced modifications in two-dimensional quantum rings
We investigate the influence of rotation on the Fermi energy, magnetization, and persistent current in two-dimensional quantum rings. Using the Tan-Inkson confinement potential and incorporating rotational effects through a non-inertial coupling, we derive analytical expressions for the energy levels and examine the modifications induced by rotation. We then numerically explore how variations in angular velocity affect the Fermi energy, magnetization, and persistent current. Our results show th…

Cyclic codes of length $n$ over finite chain rings
Seema Antil, Gurleen Kaur, Manju Khan
https://arxiv.org/abs/2509.06397 https://arxiv.org/pdf/2509.06397

Cyclic codes of length $n$ over finite chain rings
In this paper, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic group $G$ have been determined, and then the number of codewords and the minimum weight corresponding to a cyclic code have been computed.

Regularity and $\mathsf{K}_0$-Regularity under Finiteness Conditions
Rafael Parra
https://arxiv.org/abs/2509.05109 https://arxiv.org/pdf/2509.05109

Regularity and $\mathsf{K}_0$-Regularity under Finiteness Conditions
The purpose of this work is to investigate various notions of regularity from the perspective of finiteness conditions, with the ultimate goal of identifying broad classes of rings that are $\mathsf{K}_0$-regular. In this direction, we revisit the classical concepts of coherence and von Neumann regularity, and establish new characterizations. We then focus on the study of \emph{$n$-coherent regular rings}, recently introduced in [31], and analyze their $\mathsf{K}$-theoretic behavior. Finally, …

Kelce 'only interested' in SB rings, not AFC bling https://www.espn.com/nfl/story/_/id/45539848/chiefs-travis-kelce-only-interested-super-bowl-rings

Geometric properties of unit groups of von Neumann's continuous rings
Friedrich Martin Schneider
https://arxiv.org/abs/2509.01556 https://arxiv.org/pdf…

Geometric properties of unit groups of von Neumann's continuous rings
We prove that, if $R$ is an irreducible, continuous ring, then its unit group $\mathrm{GL}(R)$, equipped with the topology generated by the rank metric, is topologically simple modulo its center, path-connected, locally path-connected, bounded in the sense of Bourbaki, and not admitting any non-zero escape function. All these topological insights are consequences of more refined geometric results concerning the rank metric, in particular with regard to the set of algebraic elements. Thanks to t…

Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, Jos\'e Simental
https://arxiv.org/abs/2508.03816

Comparing cluster algebras on braid varieties
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, positroid varieties, open Bott-Samelson varieties, and Richardson varieties, among others. Recently, two cluster algebra structures were independently constructed in the coordinate rings of braid varieties: one using weaves and the other using Deodhar geometry. The main result of the article is that these two cluster alge…

Rings Whose Non-Units are Square-Nil Clean
Mina Doostalizadeh, Ahmad Moussavi, Peter Danchev
https://arxiv.org/abs/2508.01286 https://arxiv.org/pdf/2508.01…

Rings Whose Non-Units are Square-Nil Clean
We consider in-depth and characterize in certain aspects the class of so-called {\it strongly NUS-nil clean rings}, that are those rings whose non-units are {\it square nil-clean} in the sense that they are a sum of a nilpotent and a square-idempotent that commutes with each other. This class of rings lies properly between the classes of strongly nil-clean rings and strongly clean rings. In fact, it is proved the valuable criterion that a ring $R$ is strongly NUS-nil clean if, and only if, $a^4…

Some calculations of centralizer rings of a complex reflection group
Masashi Kosuda, Manabu Oura, Sarbaini
https://arxiv.org/abs/2507.20521 https://arxiv.…

Some calculations of centralizer rings of a complex reflection group
Let H1 be the complex reflection group of order 96. For the tensor products of faithful transitive permutation representations of H1, we determine the structures of the centralizer rings. This complements the work of Imamura-Kosuda-Oura.

Spectral trends across the rings and inner moons of Uranus and Neptune from JWST NIRCam images
M. M. Hedman, I. de Pater, R. Cartwright, M. El Moutamid, R. DeColibus, M. Showlater, M. S. Tiscareno, N. Rowe-Gurney, M. T. Roman, L. Fletcher, H. B. Hammel
https://arxiv.org/abs/2506.18650

Spectral trends across the rings and inner moons of Uranus and Neptune from JWST NIRCam images
JWST NIRCam images provide low-resolution spectra of the rings and inner moons orbiting Uranus and Neptune. These data reveal systematic variations in spectral parameters like the strength of the strong OH absorption band around 3 microns and the spectral slopes at continuum wavelengths. Neptune's rings show an extremely weak 3-micron band, which is likely due to the small particle sizes in these dusty rings. Neptune's small inner moons also have weaker 3-micron bands and redder continua than U…

Lensing and Photon Rings in a Magnetized Black Hole Spacetime
Muhammad Haider Khan, Volker Perlick
https://arxiv.org/abs/2508.20575 https://arxiv.org/pdf/2…

Lensing and Photon Rings in a Magnetized Black Hole Spacetime
We analyze gravitational lensing, in particular the shadow and photon rings, in the Ernst spacetime, also known as the Schwarzschild-Melvin spacetime, which describes a Schwarzschild black hole immersed in a homogenous magnetic field. Although the geodesic equation in this spacetime is chaotic, there are some relevant features that can be determined analytically. Among other things, we give analytic formulas for the vertical diameter of the shadow for an observer at arbitrary inclination and fo…

Infinitely generated symbolic Rees rings of positive characteristic
Kazuhiko Kurano
https://arxiv.org/abs/2508.04127 https://arxiv.org/pdf/2508.04127

Infinitely generated symbolic Rees rings of positive characteristic
Let X be a toric variety over a field K determined by a triangle. Let Y be the blow-up at (1,1) in X. In this paper we give some criteria for finite generation of the Cox ring of Y in the case where Y has a curve C such that C^2 \le 0 and C.E=1 (E is the exceptional divisor). The natural surjection Z^3 \rightarrow Cl(X) gives the ring homomorphism K[Z^3] \rightarrow K[Cl(X)]. We denote by I the kernel of the composite map K[x,y,z] \subset K[Z^3] \rightarrow K[Cl(X)]. Then Cox(Y) coincides with …

Metric completions of triangulated categories from hereditary rings
Cyril Matou\v{s}ek
https://arxiv.org/abs/2508.20283 https://arxiv.org/pdf/2508.20283

Metric completions of triangulated categories from hereditary rings
The focus of this article is on metric completions of triangulated categories arising in the representation theory of hereditary finite dimensional algebras and commutative rings. We explicitly describe all completions of bounded derived categories with respect to additive good metrics for two classes of rings - hereditary commutative noetherian rings and hereditary algebras of tame representation type over an algebraically closed field. To that end, we develop and study the lattice theory of m…

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- The lowest discriminant ideal of central extensions of abelian groups
Zhongkai Mi

Diamond-laden Eagles SB rings feature pop-out https://www.espn.com/nfl/story/_/id/45775422/eagles-get-super-bowl-lix-rings-sirianni-sayings

On Generalized Rickart $*$-rings
Anil Khairnar, Sanjay More
https://arxiv.org/abs/2508.20842 https://arxiv.org/pdf/2508.20842

On Generalized Rickart $*$-rings
A ring $R$ with an involution $*$ is a generalized Rickart $*$-ring if for all $x\in R$ the right annihilator of $x^n$ is generated by a projection for some positive integer $n$ depending on $x$. In this work, we introduce generalized right projection of an element in a $*$-ring and prove that every element in a generalized Rickart $*$-ring has generalized right projection. Various characterizations of generalized Rickart $*$-rings are obtained. We introduce the concept of generalized weakly Ri…

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Mackey's obstruction map for discrete graded algebras
Yuval Ginosar
https…

The Second Vanishing Theorem for Formal Local Cohomology Modules
Behruz Sadeqi
https://arxiv.org/abs/2508.05477 https://arxiv.org/pdf/2508.05477

The Second Vanishing Theorem for Formal Local Cohomology Modules
This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in terms of the dimension of the quotient ring modulo minimal primes. Our main result extends classical vanishing theorems to the formal setting, with applications to the structure of complexes in derived categories. Necessary and sufficient conditions are given via…

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Restricted graph Lie algebras in even characteristic
Simone Blumer
https://…

Crosslisted article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- The approach of cluster symmetry to Diophantine equations
Leizhen Bao, Fang Li

Eagles receive Super Bowl LIX championship rings https://www.nfl.com/news/eagles-receive-super-bowl-lix-championship-rings

Betti Numbers and Formal Local Cohomology Modules
Behruz Sadeqi
https://arxiv.org/abs/2508.05051 https://arxiv.org/pdf/2508.05051

Betti Numbers and Formal Local Cohomology Modules
This article investigates the relationship between Betti numbers of finitely generated modules over a Noetherian local ring $(R, \mathfrak{m})$ and the structure of formal local cohomology modules. We establish a connection between the vanishing of formal local cohomology and the depth of a module, generalizing classical results. The main theorem links the Betti numbers to the Artinian property of formal local cohomology modules, and we provide applications to Cohen-Macaulay rings. Original pro…

K-rings of smooth toric varieties via piecewise-exponential functions
Melody Chan, Emily Clader, Caroline Klivans, Dustin Ross
https://arxiv.org/abs/2507.13610

K-rings of smooth toric varieties via piecewise-exponential functions
We describe an explicit presentation of the ring of integral piecewise-exponential functions on a unimodular fan as a quotient of the Stanley-Reisner ring of the fan. This gives rise to a presentation of K-rings of smooth toric varieties that is parallel to the well-known presentation of integral Chow rings as quotients of Stanley-Reisner rings.

LOOK: Eagles' Super Bowl LIX rings revealed to have hidden surprise

https://www.cbssports.com/nfl/news/look-eagles-super-bowl-lix-rings-revealed-to-have-hidden-…

Big Varchenko-Gelfand rings and orbit harmonics
Brendon Rhoades
https://arxiv.org/abs/2508.18602 https://arxiv.org/pdf/2508.18602

Big Varchenko-Gelfand rings and orbit harmonics
Let $\mathscr{M}$ be a conditional oriented matroid. We define a graded algebra $\widehat{\mathscr{VG}}_\mathscr{M}$ with vector space dimension given by the number of covectors in $\mathscr{M}$ which admits a distinguished filtration indexed by the poset $\mathscr{L}(\mathscr{M})$ of flats of $\mathscr{M}$. The subquotients of this filtration are isomorphic to graded Varchenko-Gelfand rings of contractions of $\mathscr{M}$, so we call $\widehat{\mathscr{VG}}_\mathscr{M}$ the {\em graded big Va…

Hemiring-valued pseudonormed rings
Peyman Nasehpour
https://arxiv.org/abs/2508.01471 https://arxiv.org/pdf/2508.01471…

Hemiring-valued pseudonormed rings
In the second section, we introduce hemiring-valued pseudonormed rings and generalize Albert's result which states that every finite-dimensional algebra can be normed. Next, we introduce shrinkable hemirings and prove that dense division semirings are shrinkable. In the third section, we show the Cauchy Condensation Test holds for Cauchy complete fields. In the fourth section, we use Bernoulli's inequality to prove a version of ratio test for ring-valued normed groups.

[2025-06-09 Mon (UTC), 1 new article found for math.RA Rings and Algebras]
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Finiteness and infiniteness of gradings of Noetherian rings
Cheng Meng
https://arxiv.org/abs/2508.01628 https://arxiv.org/pdf/2508.01628

Finiteness and infiniteness of gradings of Noetherian rings
In this paper we show that for a torsion-free abelian group $G$, $\operatorname{rank}_\mathbb{Z}G<\infty$ if and only if there exists a Noetherian $G$-graded ring $R$ such that the set $\{R_g \neq 0\}$ generates the group $G$. For every $G$ of finite rank, we construct a $G$-graded ring $R$ such that $R_g \neq 0$ for all $g \in G$. We prove such rings give examples of PIDs which are not ED. We also use the relations between the graded division ring and the group cohomology to prove some vanishi…

[2025-09-08 Mon (UTC), 1 new article found for math.RA Rings and Algebras]
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Toroidal involutory Cayley graphs
Hamide Keshavarzi, Babak Amini, Afshin Amini, Shahin Rahimi
https://arxiv.org/abs/2508.01200 https://arxiv.org/pdf/2508.0…

Toroidal involutory Cayley graphs
Suppose that $R$ is a finite commutative ring with identity. The involutory Cayley graph $\G(R)$ of $R$ is the graph whose vertices are the elements of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if $(x-y)^2=1$. In this paper, we classify all rings $R$ for which $\G(R)$ is a toroidal graph, that is, a graph that can be embedded on a torus.

Involutory Cayley graphs of polynomial and power series rings over the ring of integers modulo $n$
Hamide Keshavarzi, Afshin Amini, Babak Amini
https://arxiv.org/abs/2508.01202 …

Involutory Cayley graphs of polynomial and power series rings over the ring of integers modulo n
Let $R$ be a commutative ring with identity. The involutory Cayley graph $\G(R)$ of $R$ is defined as the graph whose vertex set is the set of elements of $R$, where two vertices $a$ and $b$ are adjacent exactly when $(a-b)^2=1$. This paper investigates the properties of involutory Cayley graphs associated with polynomial and power series rings over the ring of integers modulo $n$.

[2025-07-09 Wed (UTC), 4 new articles found for math.RA Rings and Algebras]
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[2025-07-08 Tue (UTC), 9 new articles found for math.RA Rings and Algebras]
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[2025-08-08 Fri (UTC), 2 new articles found for math.RA Rings and Algebras]
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[2025-09-09 Tue (UTC), 6 new articles found for math.RA Rings and Algebras]
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Zero Insertive Nil Clean Rings
Sanjiv Subba, Tikaram Subedi
https://arxiv.org/abs/2508.01333 https://arxiv.org/pdf/2508.01333

Zero Insertive Nil Clean Rings
This paper investigates key properties of ZINC rings and their relationships with semicommutative and weakly semicommutative rings. We call an element $x$ of a ring $R$ zero insertive if $x=arb$ for some $a,b,r\in R$ such that $ab=0$ and $ZI(R)$ denotes the set of all zero insertive elements of $R$. We establish that a ring $R$ is semicommutative if and only if $ZI(R) \subseteq E(R)$, and weakly semicommutative if and only if $ZI(R) \subseteq N(R)$, where $E(R)$ and $N(R)$ denote respectively t…

On Generalized p.q.-Baer $*$-rings
Sanjay More, Anil Khairnar
https://arxiv.org/abs/2509.02584 https://arxiv.org/pdf/2509.02584

On Generalized p.q.-Baer $*$-rings
We introduced the class of weakly generalized p.q.-Baer $*$-rings. It is proved that under some assumptions every weakly generalized p.q.-Baer $*$-ring can be embedded in generalized p.q.-Baer $*$-ring. We proved that a generalized p.q.-Baer $*$-rings has partial comparability. If a generalized p.q.-Baer $*$-ring satisfies the parallelogram law then it is proved that every pair of projections has an orthogonal decomposition. A separation theorem for generalized p.q.-Baer $*$-rings is obtained. …

Rings with uniformly S-w-Noetherian Sspectrum
Xiaolei Zhang
https://arxiv.org/abs/2508.21403 https://arxiv.org/pdf/2508.21403

Rings with uniformly S-w-Noetherian Sspectrum
In this paper, the notion of rings with uniformly S-w-Noetherian spectrum is introduced. Several characterizations of rings with uniformly S-w-Noetherian spectrum are given. Actually, we show that a ring R has uniformly S-w-Noetherian spectrum with respect to some s 2 S if and only if each ascending chain of radical w-ideals of R is stationary with respect to s 2 S, if and only if each radical (prime) (w-)ideal of R is radically S-w-finite with respect to s, if and only if each countably genera…

Lie ideals and derivations of exceptional prime rings
Tsiu-Kwen Lee
https://arxiv.org/abs/2508.01544 https://arxiv.org/pdf/2508.01544

Lie ideals and derivations of exceptional prime rings
A prime ring $R$ with extended centroid $C$ is said to be exceptional if both $\text{\rm char}\,R=2$ and $\dim_CRC=4$. Herstein characterized additive subgroups $A$ of a nonexceptional simple ring $R$ satisfying $\big[A, [R, R]\big]\subseteq A$. In 1972 Lanski and Montgomery extended Herstein's theorem to nonexceptional prime rings. In the paper we first extend Herstein's theorem to arbitrary simple rings. For the prime case, let $R$ be an exceptional prime ring with center $Z(R)$. It is proved…

Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings
Xiaolei Zhang, Wei Qi
https://arxiv.org/abs/2508.21400 https://arxiv.org/pdf/2508.21400

Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings
In this paper, we give some new characterizations of $u$-$S$-Noetherian rings and $u$-$S$-coherent rings in terms of uniform $S$-version of injective precovers, flat preenvelopes and absolutely pure modules, respectively. Moreover, we give a negative answer to a question proposed by Bouziri [3].

Log-regularity of monoid algebras
Shinnosuke Ishiro
https://arxiv.org/abs/2509.01191 https://arxiv.org/pdf/2509.01191…

Log-regularity of monoid algebras
Local log-regular rings are Cohen-Macaulay local domains introduced by Kazuya Kato to expand the theory of toric varieties without a base. In this note, we show that local rings of monoid algebras over regular rings are log-regular.

Polynomials over division rings
Alina G. Goutor, Sergey V. Tikhonov
https://arxiv.org/abs/2509.03748 https://arxiv.org/pdf/2509.03748

Polynomials over division rings
We consider properties of polynomials with coefficients in division rings. A theorem on the decomposition of a polynomial with coefficients in an arbitrary division ring is obtained. It is shown that if a non-central element is not a root of a polynomial over an arbitrary division ring, then the conjugacy class of this element contains infinitely many elements that are not roots of this polynomial. The paper also contains estimates for the number of different conjugacy classes of spherical ro…

Skew braces, near-rings, skew rings, dirings
Alberto Facchini
https://arxiv.org/abs/2507.22182 https://arxiv.org/pdf/2507.22182

Skew braces, near-rings, skew rings, dirings
We introduce a new point of view to present classical notions related to set-theoretic solutions of the Yang-Baxter equation: left skew braces, dirings, left skew rings. The idea is, in the definition of a left near-ring $G$, to replace the multiplication of $G$ with two operations on the additive group $G$, one associative and the other left distributive. Two algebraic structures naturally appear: left skew rings and left weak rings, whose categories turn out to be canonically isomorphic.

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
- Uniformity in nonreduced rings via Noetherian operators
Yairon Cid-Ruiz, Jack Jeffries

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Homological regularities and concavities
Ellen Kirkman, Robert Won, James J. Zhang

Invariants of toric double determinantal rings
Jennifer Biermann, Emanuela De Negri, Oleksandra Gasanova, Asl{\i} Musapa\c{s}ao\u{g}lu, Sudeshna Roy
https://arxiv.org/abs/2506.22730

Invariants of toric double determinantal rings
We study a class of double determinantal ideals denoted $I_{mn}^r$, which are generated by minors of size 2, and show that they are equal to the Hibi rings of certain finite distributive lattices. We compute the number of minimal generators of $I_{mn}^r$, as well as the multiplicity, regularity, a-invariant, Hilbert function, and $h$-polynomial of the ring $R/I_{mn}^r$, and we give a new proof of the dimension of $R/I_{mn}^r$. We also characterize when the ring $R/I_{mn}^r$ is Gorenstein, there…

Rings of the right (left) almost stable range 1
Victor Bovdi, Bohdan Zabavsky
https://arxiv.org/abs/2508.21465 https://arxiv.org/pdf/2508.21465

Rings of the right (left) almost stable range 1
We introduce a concept of rings of right (left) almost stable range $1$ and we construct a theory of a canonical diagonal reduction of matrices over such rings. A description of new classes of noncommutative elementary divisor rings is done as well. In particular, for Bézout $D$-domain we introduced the notions of $D$-adequate element and $D$-adequate ring. We proved that every $D$-adequate Bézout domain has almost stable range $1$. For Hermite $D$-ring we proved the necessary and sufficient …

Elementary divisor rings with Dubrovin-Komarnytsky property
Victor Bovdi, Bohdan Zabavsky
https://arxiv.org/abs/2508.17100 https://arxiv.org/pdf/2508.17100…

Elementary divisor rings with Dubrovin-Komarnytsky property
We introduce noncommutative rings with $DK$-property (Dubrovin-Komarnytsky's property) and investigate elementary divisor rings with such property. Mostly we pay attention to these kinds of noncommutative rings which have stable range $1$. A theory of reduction matrices over such rings is constructed. As a consequence, new families of non-commutative rings of elementary divisor rings are constructed.

On Tor-vanishing of local rings
Shrikant Shekhar, Anjan Gupta
https://arxiv.org/abs/2506.21764 https://arxiv.org/pdf/2506.21764

On Tor-vanishing of local rings
Let $R$ be a local ring with residue field $k$ and $M$, $N$ be finitely generated modules over $R$. It is well known that $Tor^R_i(M, N) = 0$ for $i \gg 0$ if $pd_R(M) < \infty$ or $pd_R(N) < \infty$. The ring $R$ is said to satisfy the Tor-vanishing property if the converse holds, that is, $Tor^R_i(M, N) = 0$ for $i \gg 0$ implies $pd_R(M) < \infty$ or $pd_R(N) < \infty$. Interest in the Tor-vanishing property stems from the fact that Cohen-Macaulay local rings satisfying this property also sa…

[2025-07-07 Mon (UTC), no new articles found for math.RA Rings and Algebras]
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Radical property of the traces of the canonical modules of Cohen-Macaulay rings
Mitsuhiro Miyazaki
https://arxiv.org/abs/2506.17987 https://

Radical property of the traces of the canonical modules of Cohen-Macaulay rings
In this paper, we define a new concept of Noetherian commutative rings which stands between Gorenstein and Cohen-Macaulay properties. We show that this new property keep hold under common operations of commutative rings such as localization, polynomial extension and under mild assumptions, flat extension, tensor product, Segre product and so on. We show that for Schubert cycles, the Ehrhart rings of cycle graphs and perfect graphs, this new concept is close to Gorenstein property.

[2025-08-07 Thu (UTC), 2 new articles found for math.RA Rings and Algebras]
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Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Geometric construction of Kashiwara crystals on multiparameter persistence
Yasuaki Hiraoka, Kohei Yahiro

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- Codimension sequence, grade, and generating degree: an operadic approach
Y. -H. Bao, D. -X. Fu, J. -N. Xu, Y. Ye, J. J. Zhang, Y. -F. Zhang, Z. -B. Zhao

Leibniz rings: some basic and structural results
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
https://arxiv.org/abs/2508.17319 https://arxiv.org/pdf/2508.17…

Leibniz rings: some basic and structural results
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtained illustrate a significant difference between the classes of Leibniz rings and Lie rings.

On Strongly \( J^{\#} \)-Clean Rings
Peter Danchev, Gholamreza Karamali, Omid Hasanzadeh, Mehrdad Esfandiar
https://arxiv.org/abs/2508.17368 https://arxiv.…

On Strongly \( J^{\#} \)-Clean Rings
We define and examine the class of {\it strongly \( J^{\#} \)-clean rings} consisting of those rings $R$ such that each element of $R$ is the sum of an idempotent from $R$ and an element from $J^{\#}(R)$ that commute with each other. More exactly, we prove that these rings are simultaneously strongly clean and Dedekind-finite as well as that they factor-ring modulo the Jacobson radical is always Boolean, and also provide some close relations with certain other well-established classes of rings …

Crosslisted article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- On the probability of generating matrix incidence rings
N. A. Kolegov
http…

Some Extensions of Endo-Noetherian Rings
R. M. Salem, R. E. Abdel-Khalek, N. Abdelnasser
https://arxiv.org/abs/2507.23668 https://arxiv.org/pdf/2507.23668

Some Extensions of Endo-Noetherian Rings
In this article, we proceed on the transfer of the left endo-Noetherian property on certain ring extensions. We transfer of the right (left) endo-Noetherian property to the right (left) quotient rings. For a subring $T$ of $R$ and a finite set of indeterminates $X$, we prove that $T + XR[[X]]$ is left endo-Noetherian if and only if $R[[X]]$ is left endo-Noetherian. In addition, we prove that the subring $Λ:=\{ f \in R[[S,ω]]: f(1) \in T \}$ of the skew generalized power series ring $R[[S, ω]…