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Arbitrary models of the complete first-order theories of FDZ-rings
Mahmood Sohrabi
https://arxiv.org/abs/2603.27730 https://arxiv.org/pdf/2603.27730 https://arxiv.org/html/2603.27730
arXiv:2603.27730v1 Announce Type: new
Abstract: In this paper, we study arbitrary models of the first-order theory of a ring $A$ where the additive group $A$ is a finitely generated abelian group. Following an earlier paper by this author, Alexei G. Myasnikov and Francis Oger, we call these rings the FDZ-rings or FDZ-algebras. The rings considered are not necessarily unitary, commutative, or associative. We provide criteria for such rings to be quasi finitely axiomatizable (QFA) or bi-interpretable with the ring of integers $\mathbb Z$. We shall also describe all rings elementarily equivalent to such a ring $A$ given certain constraints on $A$.
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