Tootfinder

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

Some classes of one-dimensional rings characterized by their reflexive ideals
Pietro Campochiaro, Marco D'Anna, Francesco Strazzanti
https://arxiv.org/abs/2506.13591

Some classes of one-dimensional rings characterized by their reflexive ideals
We study reflexive ideals in one-dimensional Cohen-Macaulay local rings, providing characterizations of almost Gorenstein rings, rings with minimal multiplicity, and Arf rings, which describe their reflexive fractional ideals.

Positional numeral systems over polyadic rings
Steven Duplij
https://arxiv.org/abs/2506.12930 https://arxiv.org/pdf/2506.12930…

Positional numeral systems over polyadic rings
We construct positional numeral systems that work natively over nonderived polyadic $\left( m,n\right) $-rings whose addition takes $m$ arguments and multiplication takes $n$. In such rings, the length of an admissible additive word and a multiplicative tower are not arbitrary (as in the binary case), but \textquotedblleft quantized\textquotedblright. Our main contributions are the following. Existence: every commutative $\left( m,n\right) $-ring admits a base-$p$ place-value expansion that res…

Gravity versus astrophysics in black hole images and photon rings: equatorial emissions and spherically symmetric spacetimes
I. Urso, F. H. Vincent, M. Wielgus, T. Paumard, G. Perrin
https://arxiv.org/abs/2506.13482

Gravity versus astrophysics in black hole images and photon rings: equatorial emissions and spherically symmetric spacetimes
The EHT collaboration released in 2019 the first horizon-scale images of a black hole accretion flow, opening a novel route for plasma physics comprehension and gravitational tests. Although the present unresolved images deeply depend on the astrophysical properties of the accreted matter, GR predicts that they contain highly lensed observables, the "photon rings", embodying the effects of strong-field gravity. Focusing on the supermassive black hole M87* and adopting a geometrically thin, equa…

Settling in for another evening in Middle-earth, all thanks to Linux! Streaming Lord of the Rings Online tonight. Grab a beverage and join the relaxed adventure. #LOTROCommunity

Not only do Vertu phones still exist in 2025, I see they're now selling AI diamond smart rings.

Humpback Whales Are Approaching People to Blow Rings. What Are They Trying to Say? — Colossal
https://www.thisiscolossal.com/2025/06/humback-whales-bubble-rings/

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
Minimal operations over permutation groups
https://

Hermitian Cubic norm structures and groups of relative rank one
Michiel Smet
https://arxiv.org/abs/2506.14509 https://arxiv.org/pdf/2…

Hermitian Cubic norm structures and groups of relative rank one
Hermitian cubic norm structures were recently introduced in order to study the class of skew-dimension one structurable algebras (which are typically only defined over fields of characteristic different from $2$ and $3$) over arbitrary rings and fields. Here, we generalize the quartic norm for these algebras and show that elements for which the quartic norm is invertible are conjugate invertible. This leads to the notion of a division hermitian cubic norm structure, defined as one in which the …

Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring
Eric I. Corwin, Nikolaus Elsaesser, Axel Saenz
https://arxiv.org/abs/2506.14171

Coordinate-energy transformation and the one-point function for the Heisenberg-Ising XXZ spin-1/2 chain on the ring
We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive approach to show that the Bethe Ansatz is complete. The transformation formula is verified numerically with excellent accuracy for non-zero anisotropy parameters and rings of odd length. Additionally, assuming the Bethe Ansatz is complete, we derive a novel exact f…

On the core and adjoint of the product of complete ideals in two-dimensional regular local rings
Clare D'Cruz, Saipriya Dubey, Jugal K. Verma
https://arxiv.org/abs/2506.14228 …

On the core and adjoint of the product of complete ideals in two-dimensional regular local rings
Using joint reductions of complete ideals, we find expressions for the core and adjoints of the product of complete ideals in a two-dimensional regular local ring. We also compute their colengths. Our results strengthen a generalization of the Briançon-Skoda theorem due to D. Rees and J. D. Sally.

The fine structure of the mean magnetic field in M31
Indrajit Paul, R. Vasanth Kashyap, Tuhin Ghosh, Rainer Beck, Luke Chamandy, Srijita Sinha, Anvar Shukurov
https://arxiv.org/abs/2506.13954

The fine structure of the mean magnetic field in M31
To explore the spatial variations of the regular (mean) magnetic field of the Andromeda galaxy (M31), we use Fourier analysis in azimuthal angle along four rings in the galaxy's plane. Earlier analyses indicated that the axisymmetric magnetic field (azimuthal Fourier mode $m=0$) is sufficient to fit the observed polarization angles in a wide range of galactocentric distances. We apply a Bayesian inference approach to new, more sensitive radio continuum data at $λ\lambda3.59$, $6.18$, and $11.3…

N\'eel vector controlled exceptional contours in $p$-wave magnet-ferromagnet junctions
Md Afsar Reja, Awadhesh Narayan
https://arxiv.org/abs/2506.12434

Néel vector controlled exceptional contours in $p$-wave magnet-ferromagnet junctions
Non-Hermitian systems can host exceptional degeneracies where not only the eigenvalues, but also the corresponding eigenvectors coalesce. Recently, $p$-wave magnets have been introduced, which are characterized by their unusual odd parity. In this work, we propose the emergence of non-Hermitian degeneracies at the interface of $p$-wave magnets and ferromagnets. We demonstrate that this setup offers a remarkable tunability allowing realization of exceptional lines and rings, which can be control…

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
Two axes in non-commutative algebras with a Frobenius form
https:/…

A Davenport Constant for Integral Domains
Jared Kettinger
https://arxiv.org/abs/2506.13532 https://arxiv.org/pdf/2506.13532

A Davenport Constant for Integral Domains
In this paper, we explore an invariant of a subring which is closely related to the Davenport constant of a group. Focusing primarily on orders of rings of integers, we will calculate this constant for an important class of rings and their orders, and use it to understand factorization properties of the latter. To this end, we also define and examine the well-behaved class of stable orders.

Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings
Daniel P. Bossaller, Hiram H. L\'opez
https://arxiv.org/abs/2506.09017

Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings
Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across several nodes. If one of the nodes fails, a linear exact repair scheme efficiently recovers the failed node by accessing and downloading data from the rest of the servers of the storage system. In this article, we develop a linear repair scheme for free maxi…

I love how the “#ColeValley Town Square” pop-up turns Carl St. into a relaxed oasis. It’s a great proof-of-concept for permanently closing the street where the #NJudah emerges from the Sunset Tunnel (and extending the footprint of Gamble Memorial Park).

Constraints on Quaoar's rings and atmosphere from JWST/NIRCam observations of a stellar occultation
Benjamin Proudfoot, Bryan Holler, Ko Arimatsu, Flavia Rommel, Cameron Collyer, Estela Fern\'andez-Valenzuela
https://arxiv.org/abs/2506.07898

Constraints on Quaoar's rings and atmosphere from JWST/NIRCam observations of a stellar occultation
Observations of stellar occultations have revealed that small bodies are capable of hosting ring systems. The trans-Neptunian object (TNO) Quaoar, is the host of an enigmatic ring system, with two rings located well-outside the Roche limit. To better understand these structures, we observed a stellar occultation by Quaoar and its rings using the James Webb Space Telescope's (JWST) NIRCam instrument. Our observations detect both known rings, although Q2R -- the inner known ring -- is not detecte…

Spatial and temporal evolutions of blue-core helicon discharge driven by planar antenna with concentric rings
Chao Wang, Lei Chang, Ling-Feng Lu, Shunjiro Shinohara, Zhi-De Zeng, Ilya Zadiriev, Elena Kralkina, Zhi Li, Shi-Jie Zhang, Zi-Chen Kan, Ye Tao, Ding-Zhou Li
https://arxiv.org/abs/2506.10493…

Spatial and temporal evolutions of blue-core helicon discharge driven by planar antenna with concentric rings
The spatial and temporal evolutions of blue-core helicon discharge driven by a planar antenna with four concentric rings are explored on the Linear Experimental Advanced Device (LEAD). The discharge experiences distinct density jumps from E mode to H mode, W mode, and blue-core mode, when RF input power increases. This is similar to previous observations using other typical helicon antennas; however, this special antenna could drive modes of even higher levels for which the blue-core plasma col…

The number of maximal matchings in polygon rings
Chengqi Li, Jinhui Yin, Lingjuan Shi
https://arxiv.org/abs/2506.08687 https://arxiv.…

The number of maximal matchings in polygon rings
A matching of graph $G$ is maximal if it cannot be expanded by adding any edge to create a larger matching. In this paper, for a hexagonal ring $H$ with $n$ hexagons, we show that the number of maximal matchings of $H$ equals to the trace of the product of $n$ matrices, each of which is $S$, $L$, or $R$ according to the type of the connection mode of $H$. Finally, we extend this conclusion to arbitrary polygon rings and provide an algorithm to determine the transition matrices of polygon chains…

This https://arxiv.org/abs/2505.04760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Isotropic Torsors on Smooth Algebras over Prüfer Rings
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of Česnavičius and Fedorov, we prove a non-noetherian analogue of this conjecture for rings $A$ that are semilocalisations of smooth schemes over valuation rings of rank one, and for reductive $A$-group schemes $G$ that are totally isotropic. Roughly speaking, such group schemes are characterised by the existence of a par…

📌 Pinned Introduction
Hey, I’m Erik. I’m an anarchist with an embarrassingly massive crush on Rudolf Rocker’s syndicalist take. I’m also bisexual, autistic, and genderfluid because why not add some extra flavor?
I’m here to share my weird little world, build some solidarity, and maybe spark a little revolution along the way. No pressure, no drama, just good vibes and a lot of laughs. You do you and I’ll do me. Cool? Cool.

As a general rule, I think maybe we should stop naming companies after things from Lord of the Rings.

Photon rings in a holographic toy model
St\'ephane Detournay, Sahaja Kanuri, Alexandru Lupsasca, Philippe Spindel, Quentin Vandermiers, Raphaela Wutte
https://arxiv.org/abs/2506.07989

Photon rings in a holographic toy model
Light circling around an astrophysical black hole can spend a long time skirting its unstably bound photon orbits before escaping to infinity. To a distant observer, this orbiting light would appear as a bright ring encircling the image of the black hole. Though not yet resolved by radio-interferometric observations from the ground, this ``photon ring'' will be the target of future space-based black hole observations. Motivated by this experimental prospect, studies have sought to elucidate the…

The return of web rings.
https://serverless.industries/2025/05/27/webring.en.html

Upper cluster structure on Kac--Moody Richardson varieties
Huanchen Bao, Jeff York Ye
https://arxiv.org/abs/2506.10382 https://arxiv.…

Upper cluster structure on Kac--Moody Richardson varieties
We show coordinate rings of open Richardson varieties are upper cluster algebras for any symmetrizable Kac--Moody type. We further show the coordinate rings of (generalized) open Richardson varieties on the twisted product of flag varieties are upper cluster algebras for any symmetrizable Kac--Moody type. This includes, as special cases, reduced double Bruhat cells, Bott-Samelson varieties, braid varieties. Our results generalize various results by Casals--Gorsky--Gorsky--Le--Shen--Simental and…

[2025-06-17 Tue (UTC), 3 new articles found for math.RA Rings and Algebras]
toXiv_bot_toot

For my next modern culture and media studies work, I'd like to use "THE SIMPLE NEW SOCIO-ECONOMICGEOPOLITICALBIO-HISTORICAL APPROACH" (TSR 1987)
(The eighties were a very weird time, y'all.)
(I found this in WCA #26, ZODIAC ATTACK)

This https://arxiv.org/abs/2407.00903 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Implementation and topological characterization of Weyl exceptional rings in quantum-mechanical systems
Non-Hermiticity can lead to the emergence of many intriguing phenomena that are absent in Hermitian systems, enabled by exceptional topological defects, among which Weyl exceptional rings (WER) are particularly interesting. The topology of a WER can be characterized by the quantized Berry phase and a nonzero Chern number, both encoded in the eigenvectors of the non-Hermitian Hamiltonian. So far, WERs have been realized with classical wave systems, whose eigenvectors can be well described by cla…

[2025-06-18 Wed (UTC), 2 new articles found for math.RA Rings and Algebras]
toXiv_bot_toot

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new
[1/1]:
Arithmetic of cuts in ordered abelian groups and of ideals over valuation rings

Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
Sanjit Bhowmick, Kuntal Deka, Alexandre Fotue Tabue, Edgar Mart\'inez-Moro
https://arxiv.org/abs/2506.10381

Trace duality and additive complementary pairs of additive cyclic codes over finite chain rings
This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are free modules. Moreover, we present a necessary and sufficient condition for a pair of additive cyclic codes over a finite commutative ring to form an additive complementary pair. Finally, we construct a complementary pair of additive cyclic codes over a finite…

It‘s #TuneTuesday, the theme is #NotMyCircusNotMyMonkeys, and my brain went straight to
‘Is it any wonder why princes and kings
Are clowns that caper in their sawdust rings?
Ordinary people that are like you and me?
We're the builders of their destiny’
I …

🇺🇦 #NowPlaying on KEXP's #VarietyMix
Phoebe Rings:
🎵 Aseurai
#PhoebeRings
https://phoeberings.bandcamp.com/track/aseurai-2

Homological invariant properties under cleft extensions
Li Liang, Yajun Ma, Gang Yang
https://arxiv.org/abs/2506.02691 https://arxiv.…

Homological invariant properties under cleft extensions
We study the behavior of the Gorenstein weak global dimension and Gorenstein flat-cotorsion global dimension under a cleft extension of rings; we prove that under some mild conditons the finiteness of the Gorenstein weak global dimension and that of the Gorenstein flat-cotorsion global dimension are both invariant. Moreover, we compare the relative singularity categories with respect to flat-cotorsion modules under a cleft extension of rings. Some applications to θ-extensions and Morita contex…

Welcome to Italian Day on The Drive 2025
#CommercialDrive #vancouver

Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings
Sarah Anderson, Mike Axtell, Brenda Kroschel, Joe Stickles
https://arxiv.org/abs/2506.02953

Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings
Zero-divisor graphs of commutative rings are well-represented in the literature. In this paper, we consider dominating sets, total dominating sets, domination numbers and total domination numbers of zero-divisor graphs. We determine the domination and total domination numbers of zero-divisor graphs are equal for all zero-divisor graphs of commutative rings except for $\mathbb{Z}_2 \times D$ in which $D$ is a domain. In this case, $γ(Γ(\mathbb{Z}_2 \times D)) = 1$ and $γ_t(Γ(\mathbb{Z}_2 \ti…

This https://arxiv.org/abs/2412.03283 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Black-Box Forgery Attacks on Semantic Watermarks for Diffusion Models
Integrating watermarking into the generation process of latent diffusion models (LDMs) simplifies detection and attribution of generated content. Semantic watermarks, such as Tree-Rings and Gaussian Shading, represent a novel class of watermarking techniques that are easy to implement and highly robust against various perturbations. However, our work demonstrates a fundamental security vulnerability of semantic watermarks. We show that attackers can leverage unrelated models, even with differen…

This https://arxiv.org/abs/2412.19295 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Random matrix statistics and zeroes of $L$-functions via probability in $λ$-rings
We introduce a theory of probability in $λ$-rings designed to efficiently describe random variables valued in multisets of complex numbers, varieties over a field, or other similar enriched settings. A key role is played by the $σ$-moment generating function based on the plethystic exponential, which allows us to describe distributions and argue with independence in a way that is as simple as classical probability theory. As a first application, we use this theory to obtain a concise descript…

On Tameness, Measurability and the Independence Property
Lothar Sebastian Krapp, Matthieu Vermeil, Laura Wirth
https://arxiv.org/abs/2506.08733 https://

On Tameness, Measurability and the Independence Property
In the area of Tame Geometry, different model-theoretic tameness conditions are established and their relationships are analyzed. We construct a subfield $K$ of the real numbers that lacks several of such tameness properties. As our main result, we present a first-order formula in the language of rings that defines a non-Borel set in $K$. Moreover, $K$ has the independence property and admits both archimedean and non-archimedean orderings.

This https://arxiv.org/abs/2410.23052 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the Tambara Affine Line
Tambara functors are the analogue of commutative rings in equivariant algebra. Nakaoka defined ideals in Tambara functors, leading to the definition of the Nakaoka spectrum of prime ideals in a Tambara functor. In this work, we continue the study of the Nakoaka spectra of Tambara functors. We describe, in terms of the Zariski spectra of ordinary commutative rings, the Nakaoka spectra of many Tambara functors. In particular: we identify the Nakaoka spectrum of the fixed point Tambara functor of …

The Dixmier problem for skew PBW extensions and rings
William Fajardo, Oswaldo Lezama
https://arxiv.org/abs/2506.09285 https://arxiv.…

The Dixmier problem for skew PBW extensions and rings
In this paper we discuss for skew $PBW$ extensions the famous Dixmier problem formulated by Jacques Dixmier in 1968. The skew $PBW$ extensions are noncommutative rings of polynomial type and covers several algebras and rings arising in mathematical physics and noncommutative algebraic geometry. For this purpose, we introduce the Dixmier algebras and we will study the Dixmier problem for algebras over commutative rings, in particular, for $\mathbb{Z}$-algebras, i.e., for arbitrary rings. The res…

The Bloch-Ogus Theorem over DVR
Ivan Gaidai-Turlov
https://arxiv.org/abs/2506.06892 https://arxiv.org/pdf/2506.06892

The Bloch-Ogus Theorem over DVR
We prove the Bloch-Ogus Theorem for regular local rings geometrically regular over a discrete valuation ring. In particular, we prove the Bloch-Ogus Theorem for regular local rings of mixed characteristic that are essentially smooth over a discrete valuation ring.

Relative Inverse Limit Perfection of Derived Commutative Rings
Daniel Fink
https://arxiv.org/abs/2506.10626 https://arxiv.org/pdf/250…

Relative Inverse Limit Perfection of Derived Commutative Rings
We study the relative Frobenius map associated with a map of derived commutative rings over a field of positive characteristic. As part of this, we examine a relative analog of perfectness and construct a relative inverse limit perfection which, under suitable conditions on the base, serves as a right adjoint to the inclusion of relatively perfect algebras into the category of all algebras. Specializing to animated rings, we investigate relative versions of semiperfectness and F-finiteness, and…

My colleague had a question about rational functions that needed a little algebra to answer, leading me to update my supplemental course notes on abstract algebra (where I've used the Beachy/Blair textbook). A main goal of the notes is to stake out my position on the notation for rngs vs. rings.
https://use…

This https://arxiv.org/abs/2505.13647 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On $z^\circ$-ideals and annihilator ideals
For $a\in R$, let $P_a$ denote the intersection of all minimal prime ideals of $R$ containing $a$. An ideal $I$ of a ring $R$ is called a $z^{\circ}$-ideal if $P_a\subseteq I$ for all $a\in I$. In this paper, we first investigate the class of $z^{\circ}$-ideals in non-commutative rings. We provide characterizations of $z^{\circ}$-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangular matrix rings, and semiprime rings. Next, we explore new properties of the lattice $rAnn…

Acyclic complexes and regular rings
Lars Winther Christensen, Sergio Estrada, Peder Thompson
https://arxiv.org/abs/2506.09831 https://

Acyclic complexes and regular rings
A 2009 paper by Iacob and Iyengar characterizes noetherian regular rings in terms of properties of complexes of projective modules, flat modules, and injective modules. We show that the relevant properties of such complexes are equivalent without reference to regularity of the ring and that they characterize coherent regular rings and von Neumann regular rings.

This https://arxiv.org/abs/2505.19153 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Grothedieck rings of rank $4$ self-dual fusion categories
Let $\C$ be a self-dual fusion category of rank $4$ which has a nontrivial proper fusion subcategory. We identify three new families of Grothendieck rings for $\C$, each parameterized by several non-negative integers.

Multivariable period rings of $p$-adic false Tate curve extension
Yijun Yuan
https://arxiv.org/abs/2505.24064 https://arxiv.org/pdf/2…

Multivariable period rings of $p$-adic false Tate curve extension
Let $p\geq 3$ be a prime number and $K$ be a finite extension of $\mathbf{Q}_p$ with uniformizer $π_K$. In this article, we introduce two multivariable period rings $\mathbf{A}_{\mathfrak{F},K}^{\operatorname{np}}$ and $\mathbf{A}_{\mathfrak{F},K}^{\operatorname{np},\operatorname{c}}$ for the étale $(φ,Γ_{\mathfrak{F},K})$-modules of $p$-adic false Tate curve extension $K\left(π_K^{1/p^\infty},ζ_{p^\infty}\right)$. Various properties of these rings are studied and as applications, we show…

Quasi-Closed-Form Driven Near-Field Flat-Top Beamfocusing with Concentric Circular Vertical Polarized Dipole Array For Large Intelligent Surface Applications
Jiawang Li
https://arxiv.org/abs/2506.07678

Quasi-Closed-Form Driven Near-Field Flat-Top Beamfocusing with Concentric Circular Vertical Polarized Dipole Array For Large Intelligent Surface Applications
This letter presents a near-field flat-top beam synthesis method based on a semi-closed-form approach. First, the feasibility of achieving a flat-top beam in the near field is examined using a closed-form analysis. A circular concentric ring array structure is adopted, and it is observed that circular rings with different radii exhibit distinct gain characteristics along the focal region on the z-axis. Specifically, smaller radii lead to a monotonic increase in electric field strength near the …

Curious humpback whales approach humans and blow bubble 'smoke' rings
https://phys.org/news/2025-06-curious-humpback-whales-approach-humans.html

Replaced article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
Group actions and automorphisms of evolution algebras associated to finite graphs

Weekend #Plankton Factoid 🦠🦐
There is a giant, vibrantly blue, 9 meter tall, 20 tonne interactive #sculpture celebrating stromatolites (fossil cyanobacteria) in Cornwall, England. The Eden Project houses this fantastic piece of art by Azusa Murakami and Alexander Groves called "infinity blu…

The Near-Centaur Environment: Satellites, Rings, and Debris
A. A. Sickafoose, S. M. Giuliatti Winter, R. Leiva, C. B. Olkin, D. Ragozzine, L. M. Woodney
https://arxiv.org/abs/2506.04130

The Near-Centaur Environment: Satellites, Rings, and Debris
The unexpected finding of a ring system around the Centaur (10199) Chariklo opened a new window for dynamical studies and posed many questions about the formation and evolutionary mechanisms of Centaurs as well as the relationship to satellites and outbursting activity. As minor planets that cross the orbits of the giant planets, Centaurs have short dynamical lifetimes: Centaurs are supplied from the trans-Neptunian region and some fraction migrates inward to become Jupiter-family comets. Given…

Burgers rings as topological signatures of Eshelby-like plastic events in glasses
Arabinda Bera, Ido Regev, Alessio Zaccone, Matteo Baggioli
https://arxiv.org/abs/2505.23069

Burgers rings as topological signatures of Eshelby-like plastic events in glasses
Eshelby-like quadrupolar structures serve as the fundamental microscopic units for characterizing plastic instabilities in amorphous solids and play a crucial role in explaining their mechanical failure, including the formation of shear bands. However, identifying Eshelby-like plastic events in glasses remains challenging due to their inherent structural and dynamical complexity. In this work, we show that Eshelby-like structures can be precisely identified and localized using a topological inv…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Phoebe Rings:
🎵 Fading Star
#PhoebeRings
https://phoeberings.bandcamp.com/track/fading-star
https://open.spotify.com/track/20ka6zZLlIEieG7MbW3TZ3

On ideals of product of commutative rings and their applications
Mehdi Badie, Ali Rezaie Aliabad, Foad Obeidavi
https://arxiv.org/abs/2506.08537 https://…

On ideals of product of commutative rings and their applications
In this paper, leveraging the recent achievements of researchers, we have revisited the family of ideals of product of commutative rings. We demonstrate that if $ \{ R_α\}_{α\in A} $ is an infinite family of rings, then $ \left| Max \left( \prod_{α\in A} R_α\right) \right| \geqslant 2^{2^{|A|}} $. Notably, if these rings are local then the equality holds. We establish that $ Max(R_α) $ is homeomorphic to a closed subset of $ Max \left( \prod_{α\in A} R_α\right) $, for…

Families of Green rings for abelian restricted Lie algebras
Justin Bloom
https://arxiv.org/abs/2506.02388 https://arxiv.org/pdf/2506.…

Families of Green rings for abelian restricted Lie algebras
We find equivalent conditions determining the representation type of abelian restricted Lie algebras in terms of how their Green ring of restricted representations varies with respect to different cocommutative Hopf algebra structures on its restricted universal enveloping algebra. Each compatible cocommutative Hopf algebra structure on a tame algebra is shown to have a correspondence between a certain set of Hopf subalgebras, and the set of minimal thick tensor-ideals having identical ring str…

#uspol #lotr

Discovery of Odd Radio Circles and Other Peculiars in the First Year of the EMU Survey using Object Detection
Nikhel Gupta, Ray P. Norris, Zeeshan Hayder, Minh Huynh, Heinz Andernach, Andrew M. Hopkins, Stanislav Shabala, Lawrence Rudnick, Miroslav D. Filipovi\'c, B\"arbel S. Koribalski, Lars Petersson, X. Rosalind Wang
https://

Discovery of Odd Radio Circles and Other Peculiars in the First Year of the EMU Survey using Object Detection
We present a systematic search for Odd Radio Circles (ORCs) and other unusual radio morphologies using data from the first year of the EMU (Evolutionary Map of the Universe) survey. ORCs are rare, enigmatic objects characterized by edge-brightened rings of radio emission, often found in association with distant galaxies. To identify these objects, we employ a hybrid methodology combining supervised object detection techniques and visual inspection of radio source candidates. This approach leads…

Determining unit groups and $\mathrm{K}_1$ of finite rings
Tommy Hofmann
https://arxiv.org/abs/2506.00266 https://arxiv.org/pdf/2506.…

Determining unit groups and $\mathrm{K}_1$ of finite rings
We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first $K$-group of finite rings.

Canonical traces of fiber products and their applications
Shinya Kumashiro, Sora Miyashita
https://arxiv.org/abs/2506.04899 https://a…

Canonical traces of fiber products and their applications
We study the canonical trace of the fiber product of Noetherian rings. Furthermore, we extend results on the class of Cohen-Macaulay rings called Teter type to Noetherian rings. As an application of our study on canonical traces and Noetherian rings of Teter type, we compute the canonical trace of the Stanley-Reisner ring arising from a non-connected simplicial complex. In particular, we provide a characterization of Stanley-Reisner rings for which the canonical trace contains the graded maxima…

Beilinson--Lichtenbaum phenomenon for motivic cohomology
Tess Bouis, Arnab Kundu
https://arxiv.org/abs/2506.09910 https://arxiv.org/p…

Beilinson--Lichtenbaum phenomenon for motivic cohomology
The goal of this paper is to study non-$\mathbb{A}^1$-invariant motivic cohomology, recently defined by Elmanto, Morrow, and the first-named author, for smooth schemes over possibly non-discrete valuation rings. We establish that the cycle class map from $p$-adic motivic cohomology to a suitable truncation of Bhatt--Lurie's syntomic cohomology is an isomorphism, thereby verifying the Beilinson--Lichtenbaum conjecture in this generality. As a consequence, we prove that this motivic cohomology in…

On $z^\circ$-ideals and annihilator ideals
A. Taherifar
https://arxiv.org/abs/2505.13647 https://arxiv.org/pdf/2505.13647

On $z^\circ$-ideals and annihilator ideals
For $a\in R$, let $P_a$ denote the intersection of all minimal prime ideals of $R$ containing $a$. An ideal $I$ of a ring $R$ is called a $z^{\circ}$-ideal if $P_a\subseteq I$ for all $a\in I$. In this paper, we first investigate the class of $z^{\circ}$-ideals in non-commutative rings. We provide characterizations of $z^{\circ}$-ideals in 2-by-2 generalized triangular matrix rings, full and upper triangular matrix rings, and semiprime rings. Next, we explore new properties of the lattice $rAnn…

This https://arxiv.org/abs/2308.09696 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings
The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other one. In this paper, the metric dimension of $In(R)$ is discussed. Moreover, the structure of the resolving graph of $In(R)$ is characterized and as an application, we compute the strong metric dimension of $In(R)$.

This https://arxiv.org/abs/2409.18947 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Smooth geometry of skew PBW extensions over commutative polynomial rings I
In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.

Deformations of pseudocharacters and Mazur's finiteness condition
Vytautas Pa\v{s}k\=unas, Julian Quast
https://arxiv.org/abs/2506.10901 https://

Deformations of pseudocharacters and Mazur's finiteness condition
We show that deformation rings $R^{\mathrm{ps}}$ of $G$-pseudocharacters of a profinite group $Γ$ are noetherian, when $Γ$ satisfies Mazur's finiteness condition. The proof proceeds by reduction to the case when $Γ$ is finitely generated, where the result was previously established by the second author. This enables us to extend our work on moduli spaces of $R^{\mathrm{ps}}$-condensed representations of a finitely generated profinite group $Γ$, to the groups satisfying Mazur's finiteness co…

This https://arxiv.org/abs/2502.09543 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The main jet axis of the W49B supernova remnant
We identify an axis connecting two opposite `ears' in the supernova remnant W49B and morphological signatures of three arcs around this axis that we claim are sections of full circum-jet rings. Based on recent identifications of morphological signatures of jets in core-collapse supernovae (CCSNe), including ejecta-rich axes, we reexamine images of W49B and identify a heavy element-rich protrusion (ear) as a jet-inflated structure. We identify the opposite ear and a clump at its tip as the signa…

[2025-06-16 Mon (UTC), 3 new articles found for math.RA Rings and Algebras]
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Real syntomic cohomology
Gabriel Angelini-Knoll, Hana Jia Kong, J. D. Quigley
https://arxiv.org/abs/2505.24734 https://arxiv.org/pdf/…

Real syntomic cohomology
We introduce a theory of syntomic cohomology for ring spectra with involution, which we call Real syntomic cohomology. We show that our construction extends the theory of syntomic cohomology for rings with involution due to Park. Our construction also refines syntomic cohomology as developed by Bhatt--Morrow--Scholze, Morin, Bhatt--Lurie, and Hahn--Raksit--Wilson. We compute the Real syntomic cohomology of Real topological K-theory and topological modular forms with level structure.

Maximal minors of $1$-generic matrices have rational singularities
Trung Chau, Manoj Kummini
https://arxiv.org/abs/2506.08385 https://

Maximal minors of $1$-generic matrices have rational singularities
We show that the quotient ring by the ideal of maximal minors of a $1$-generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are normal, and generalizes a result of Conca, Mostafazadehfard, Singh and Varbaro (2018) that generic Hankel determinantal rings have rational singularities in characteristic zero.

Some Properties of Twisted Chevalley Groups
Deep H. Makadiya
https://arxiv.org/abs/2505.24430 https://arxiv.org/pdf/2505.24430…

Some Properties of Twisted Chevalley Groups
This thesis investigates certain structural properties of twisted Chevalley groups over commutative rings, focusing on three key problems. Let $R$ be a commutative ring satisfying mild conditions. Let $G_{π,σ} (Φ, R)$ denote a twisted Chevalley group over $R$, and let $E'_{π, σ} (Φ, R)$ denote its elementary subgroup. The first problem concerns the normality of $E'_{π, σ} (Φ, R, J)$, the relative elementary subgroups at level $J$, in the group $G_{π, σ} (Φ, R)$. The second problem…

The Chow Ring of the 2-Sylow Subgroup of $\mathrm{GL}(4,2)$
Alexander Ziegler
https://arxiv.org/abs/2506.06512 https://arxiv.org/pdf/…

The Chow Ring of the 2-Sylow Subgroup of $\mathrm{GL}(4,2)$
This paper provides a computation of the mod 2 Chow ring of the motivic étale classifying space of the finite group $\mathrm{Syl}_2(\mathrm{GL}(4,2))$. It outlines a general computation strategy, adapted from work by Burt Totaro, that has been largely automated by the author. This strategy can be used to compute more examples of Chow rings of motivic étale classifying spaces quickly.

This https://arxiv.org/abs/2407.14624 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Waring Numbers of Ramified $p$-adic Rings
Let $p$ be prime and $e,k$ be positive integers, and let $R = {\mathbb Z}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p, e$, and $k$, and investigate how the Waring numbers for $p=2$ change as $e$ and $k$ vary.

The probability that the product of k elements in a finite ring is zero
Dibyasman Sarma, Tikaram Subedi
https://arxiv.org/abs/2506.10392 https://

The probability that the product of k elements in a finite ring is zero
In this paper, for a fixed integer $k\ge 2$, we study the probability that the product of $k$ randomly chosen elements in a finite commutative ring $R$ is zero, which we denote by $zp_{_k}(R)$. We investigate bounds for $zp_{_k}(R)$ that turn out to be sharp bounds for certain classes of rings. Further, we determine the maximum value of $zp_{_k}(R)$ that can be obtained for any ring $R$, and classify all rings within some specific range of $zp_{_k}(R)$.

Replaced article(s) found for math.AC. https://arxiv.org/list/math.AC/new/
[1/1]:
When do pseudo-Gorenstein rings become Gorenstein?
https://

This https://arxiv.org/abs/2501.00394 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Cluster algebras and quantum cohomology rings: A-type
We construct a cluster algebra structure within the quantum cohomology ring of a quiver variety associated with an $A$-type quiver. Specifically, let $Fl:=Fl(N_1,\ldots,N_{n+1})$ denote a partial flag variety of length $n$, and $QH_S^*(Fl)[t]:=QH_S^*(Fl)\otimes \mathbb C[t]$ be its equivariant quantum cohomology ring extended by a formal variable $t$, regarded as a $\mathbb Q$-algebra. We establish an injective $\mathbb Q$-algebra homomorphism from the $A_n$-type cluster algebra to the algebra …

The embedded deformation problem for monomial ideals
Benjamin Briggs, Elo\'isa Grifo, Josh Pollitz
https://arxiv.org/abs/2506.10827 https://

The embedded deformation problem for monomial ideals
This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article positively answers a question of Avramov for such a ring $R$. More precisely, we establish that an embedded deformation of $R$ corresponds exactly to a degree two central element in the homotopy Lie algebra of $R$, as well as a free summand of the conormal module of $R$. A major input in the proof is an analysis of cohomol…

This https://arxiv.org/abs/2503.16393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity $=$ Volume formula and Newton non-degenerate ideals in regular local rings
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We show that the characterization of NND ideals via their integral closures known in the analytical setting extends to regular local rings. We use the limiting body $\mathcal{C}(\mathcal{I})$ associated to a graded family $\mathcal{I}$ of ideals to provide a new understanding of the celebrated "Multiplicity $=$ Volume" f…

[2025-06-13 Fri (UTC), 2 new articles found for math.RA Rings and Algebras]
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This https://arxiv.org/abs/2408.11643 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

K3 surfaces with maximal complex multiplication
Following Valloni, we study complex projective K3 surfaces having complex multiplication by rings of integers.

This https://arxiv.org/abs/2503.16393 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Multiplicity $=$ Volume formula and Newton non-degenerate ideals in regular local rings
We develop the notions of Newton non-degenerate (NND) ideals and Newton polyhedra for regular local rings. These concepts were first defined in the context of complex analysis. We show that the characterization of NND ideals via their integral closures known in the analytical setting extends to regular local rings. We use the limiting body $\mathcal{C}(\mathcal{I})$ associated to a graded family $\mathcal{I}$ of ideals to provide a new understanding of the celebrated "Multiplicity $=$ Volume" f…

This https://arxiv.org/abs/2412.17187 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generalized Homogeneous Derivations of Graded Rings
In this manuscript, we introduce a novel concept in graded rings called generalized homogeneous derivations, which serve as a natural generalization of the homogeneous derivations introduced by Kanunnikov. We establish the specialized notion of gr-generalized derivations, a subclass that preserves the degree of homogeneous elements. We extend several significant results, originally established for prime rings, to the context of gr-prime rings. Furthermore, we characterize when gr-semiprime ring…

Cohomological support varieties under local homomorphisms
Ryan Watson
https://arxiv.org/abs/2506.10757 https://arxiv.org/pdf/2506.107…

Cohomological support varieties under local homomorphisms
Given a bounded complex of finitely generated modules $M$ over a commutative noetherian local ring $R$, one assigns to it a variety, $\mathcal V_R(M)$, called the cohomological support variety of $M$ over $R$. The variety $\mathcal V_R(M)$ holds important homological information about the complex and the ring. In this paper, we study the behavior of cohomological support varieties under restriction of scalars along local maps. In the case where the rings involved are complete intersections and …

This https://arxiv.org/abs/2505.15707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

When are syzygies of the residue field self-dual?
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao characterized Arf local rings as exactly those one-dimensional Cohen--Macaulay local rings over which every finitely generated reflexive module is self-dual, and raised the general question of characterizing rings over which every finitely generated reflexive module…

[2025-06-12 Thu (UTC), 2 new articles found for math.RA Rings and Algebras]
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This https://arxiv.org/abs/2505.15707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

When are syzygies of the residue field self-dual?
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao characterized Arf local rings as exactly those one-dimensional Cohen--Macaulay local rings over which every finitely generated reflexive module is self-dual, and raised the general question of characterizing rings over which every finitely generated reflexive module…

[2025-06-11 Wed (UTC), 3 new articles found for math.RA Rings and Algebras]
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This https://arxiv.org/abs/2407.19999 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Auslander-Reiten annihilators
The Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely generated module is projective when certain Ext-modules vanish. But what if those Ext-modules do not vanish? We study the annihilators of these Ext-modules and formulate a generalisation of the Auslander-Reiten Conjecture. We prove this general version for high syzygies of modules over several classes of rings including analytically unramified Arf rings, 2-dimensional local normal domains with rational sin…

Nilpotent graphs over skew PBW extensions
Sebasti\'an Higuera, Armando Reyes
https://arxiv.org/abs/2506.00632 https://arxiv.org/p…

Nilpotent graphs over skew PBW extensions
We investigate the diameter and girth of the nilpotent graph for skew PBW extensions over $2$-primal rings, generalizing similar results on skew polynomial rings. Under certain compatibility conditions, we establish bounds for the diameter of the nilpotent graph and prove invariance of the girth under polynomial extensions.

This https://arxiv.org/abs/2407.19999 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Auslander-Reiten annihilators
The Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely generated module is projective when certain Ext-modules vanish. But what if those Ext-modules do not vanish? We study the annihilators of these Ext-modules and formulate a generalisation of the Auslander-Reiten Conjecture. We prove this general version for high syzygies of modules over several classes of rings including analytically unramified Arf rings, 2-dimensional local normal domains with rational sin…

[2025-06-10 Tue (UTC), 3 new articles found for math.RA Rings and Algebras]
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[2025-06-09 Mon (UTC), 1 new article found for math.RA Rings and Algebras]
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S-r-$ideals in Commutative Rings
Abuzer G\"und\"uz, Osama A. Naji, Mehmet \"Ozen
https://arxiv.org/abs/2505.19198 https://

S-r-$ideals in Commutative Rings
This article introduces the notion of $S-r-$ideals in commutative ring $H$ as a generalization of $ r-$ideals. Let $S$ be a multiplicatively closed subset and $A$ an ideal of $H$ with $S\cap A= \emptyset$. $A$ is called $S-r-ideal$ if $ \exists s\in S$ such that for $w,z\in H,\; wz\in A$ and $Ann(w)=0$, then $sz\in A.$ Basic properties of $S-r-$ideals are given. It is shown that an $r-$ideal is always an $S-r-$ideal, and the converse is true under some conditions. Various characterizations of $…

S-r-$ideals in Commutative Rings
Abuzer G\"und\"uz, Osama A. Naji, Mehmet \"Ozen
https://arxiv.org/abs/2505.19198 https://

S-r-$ideals in Commutative Rings
This article introduces the notion of $S-r-$ideals in commutative ring $H$ as a generalization of $ r-$ideals. Let $S$ be a multiplicatively closed subset and $A$ an ideal of $H$ with $S\cap A= \emptyset$. $A$ is called $S-r-ideal$ if $ \exists s\in S$ such that for $w,z\in H,\; wz\in A$ and $Ann(w)=0$, then $sz\in A.$ Basic properties of $S-r-$ideals are given. It is shown that an $r-$ideal is always an $S-r-$ideal, and the converse is true under some conditions. Various characterizations of $…

This https://arxiv.org/abs/2307.11489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some properties of the asymptotic Samuel function
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

This https://arxiv.org/abs/2307.11489 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some properties of the asymptotic Samuel function
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

[2025-06-06 Fri (UTC), no new articles found for math.RA Rings and Algebras]
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[2025-06-05 Thu (UTC), 1 new article found for math.RA Rings and Algebras]
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This https://arxiv.org/abs/2504.21760 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounded powers of edge ideals: Gorenstein toric rings
Let $S=K[x_1, \ldots,x_n]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $\mathfrak{c}\in\mathbb{N}^n$, the ideal $I_{\mathfrak{c}}$ is the ideal generated by those monomials belonging to $I$ whose exponent vectors are componentwise bounded above by $\mathfrak{c}$. Let $δ_{\mathfrak{c}}(I)$ be the largest integer $q$ for which $(I^q)_{\mathfrak{c}}\neq 0$. For a finite graph $G$, its edge ideal is denoted by $I(G)$. Let $\mathca…