Alexei Miasnikov, Mahmood Sohrabi
In this paper we provide a complete algebraic characterization of elementary equivalence of rings with a finitely generated additive group in the language of pure rings. The rings considered are arbitrary otherwise.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this paper, we define finitely additive, probability and modular functions over semiring-like structures. We investigate finitely additive functions with the help of complemented elements of a semiring. We also generalize some classical results in probability theory such as the Law of Total Probability, Bayes' Theorem, the Equality of Parallel Systems, and Poincaré's Inclusion-Exclusion Theorem. While we prove that modular functions over a couple of known semirings are almost constant, we show it is possible to define many different modular functions over some semirings such as bottleneck a…
We prove that a commutative parasemifield S is additively idempotent provided that it is finitely generated as a semiring. Consequently, every proper commutative semifield T that is finitely generated as a semiring is either additively constant or additively idempotent. As part of the proof, we use the classification of finitely generated lattice-ordered groups to prove that a certain monoid associated to the parasemifield S has a distinguished geometrical property called prismality.
Flatness in finitely accessible additive categories
本文在有限可访问加法范畴中推广研究平坦性，刻画范畴的预阿贝尔/阿贝尔性质及具有足够平坦与投射对象的条件，并揭示平坦对象类在纯子对象下的封闭性与直并分解之间的关系。
In this short note we present an elementary matrix-constructive proof of Quillen-Suslin theorem for Ore extensions: If $K$ is a division ring and $A:=K[x;σ,δ]$ is an Ore extension, with $σ$ bijective, then every finitely generated projective $A$-module is free. We will show an algorithm that computes the basis of a given finitely generated projective module. The algorithm has been implemented in a computational package, and some illustrative examples are included.
We study relations between the additive and the multiplicative groups of a two-sided skew brace. In particular, we prove that if the additive group of a two-sided skew brace is finite solvable (respectively, finitely generated nilpotent, finitely generated residually nilpotent, finitely generated residually finite), then the multiplicative group of this skew brace is solvable (respectively, solvable, residually solvable, residually finite). Also, we prove that if the multiplicative group of a two-sided skew brace is nilpotent of nilpotency class $k$, then the additive group of this skew brace …
On the finite separability of finitely generated associative rings
本文研究有限生成结合环的有限可分性，给出单生环的充要条件，并据此刻画有限生成无挠 PI-环的有限可分性。
Additivity of Jordan Elementary Maps on Rings
证明了环上的Jordan初等满射自动可加。
Elementary Maps on Triangular Algebras
本文证明了三角代数上的初等映射是自动可加的。
Jordan Triple Elementary Maps on Rings
证明了含有非平凡幂等元的酉环上的Jordan三重初等满射是自动可加的。
On the (non)existence of states on orthogonally closed subspaces in an inner product space
假设$S$是一个不完全的内积空间。A. Dvurečenskij证明了在$S$的正交闭子空间$F(S)$上不存在相对于n维空间正则的n维加法态。在本说明中，我们表明，最重要的特殊情况下，前一结果-的情况下，评价的向量在"格里森方式“-允许一个相对简单的证明。这一结果进一步证实了在$F(S)$上根本不存在可加性态的猜想。
Rings with finitely many zero divisors
本文通过简单证明展示：具有指定有限个零因子的环必为有限环，并给出其阶的精确界。
Torsion factors of commutative monoid semirings
本文研究交换幺半群半环因子的加法性质，证明有限秩自由交换幺半群子幺半群对应的半环因子加法几乎可除当且仅当它是挠的。
Normal Quaternionic Matrices and Finitely Generated Witt Rings
本文通过四元数矩阵方法验证了抽象威特环的初等类型猜想，利用2- torsion部分验证了阿罗森-福斯特主定理，并通过计算找到n至7的矩阵结构。
The finite basis problem for matrix semirings over a two-element additively idempotent semiring
研究了二维加法幂等半环上矩阵半环的有限基性质，证明当半环不同于分配格时，矩阵半环具有有限基。
Coherence for elementary amenable groups
该研究针对初等顺从群，证明群凝聚性、同调凝聚性与整群环凝聚性等价，推广了Bieri和Strebel关于有限生成可解群的相关结论。
It is a classical result that the direct product AxB of two groups is finitely generated (finitely presented) if and only if A and B are both finitely generated (finitely presented). This is also true for direct products of monoids, but not for semigroups. The typical (counter)example is when A and B are both the additive semigroup P = {1,2,3,...} of positive integers. Here P is freely generated by a single element, but P^2 is not finitely generated, and hence not finitely presented. In this note we give an explicit presentation for P^2 in terms of the unique minimal generating set; in fact, w…
Locally coherent exact categories
本文提出局部相干正合范畴的概念，证明小幂等完备加性范畴上的正合结构可唯一扩展为 ind-objects 范畴上的局部相干正合结构，并推导出两个周期性定理。
Elementary properties of power series fields over finite fields
尽管Q_p和F_p（（t））之间的相似性通过Ax和Kochen的工作变得明显，但将他们给出的Q_p的完整递归公理系统修改为F_p（（t））的情况并不表示一个完整的公理系统。本文证明了表示可加多项式作为映射在F_p（（t））上作用的初等性质的独立性。我们制定了一个基本的属性表示这一行动，并表明，它适用于所有的极大值领域。我们还讨论了任意多项式在值域上的作用。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。