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pro vyhledávání: '"16U99"'
In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such that $mr$
Externí odkaz:
http://arxiv.org/abs/2403.13939
Autor:
Brandenburg, Martin
A classical theorem by Jacobson says that a ring in which every element $x$ satisfies the equation $x^n=x$ for some $n>1$ is commutative. According to Birkhoff's Completeness Theorem, if $n$ is fixed, there must be an equational proof of this theorem
Externí odkaz:
http://arxiv.org/abs/2310.05301
Autor:
Janssens, Geoffrey, Margolis, Leo
Jespers and Sun conjectured that if a finite group $G$ has the property ND, i.e. for any nilpotent element $n$ in the integral group ring $\mathbb{Z}G$ and any primitive central idempotent $e \in \mathbb{Q}G$ one still has $ne \in \mathbb{Z}G$, then
Externí odkaz:
http://arxiv.org/abs/2307.14820
We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.
Comment: In this new ver
Comment: In this new ver
Externí odkaz:
http://arxiv.org/abs/2304.02165
Autor:
Gou, Haibo, Chen, Huanyin
In this paper we investigate Hirano invertibility of anti-triangular matrix over a Banach algebra. Let $a\in {\mathcal A}^H, b\in {\mathcal A}^{sD}.$ If $b^Da=0, bab^{\pi}=0,$ we prove that $\begin{pmatrix} a&1\\ b&0 \end{pmatrix}\in M_2(\mathcal A)^
Externí odkaz:
http://arxiv.org/abs/2303.15146
Autor:
Zusmanovich, Pasha
Publikováno v:
Comm. Algebra 49 (2021), no.3, 1104-1119
We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.
Comment: 13
Comment: 13
Externí odkaz:
http://arxiv.org/abs/2211.06640
Autor:
Gardella, Eusebio, Thiel, Hannes
Publikováno v:
Linear Algebra Appl. 670 (2023), 121--153
We say that an algebra is zero-product balanced if $ab\otimes c$ and $a\otimes bc$ agree modulo tensors of elements with zero-product. This is closely related to but more general than the notion of a zero-product determined algebra of Bre\v{s}ar, Gra
Externí odkaz:
http://arxiv.org/abs/2210.07891
A ring $R$ is said to be i-reversible if for every $a,b$ $\in$ $R$, $ab$ is a non-zero idempotent implies $ba$ is an idempotent. It is known that the rings $M_n(R)$ and $T_n(R)$ (the ring of all upper triangular matrices over $R$) are not i-reversibl
Externí odkaz:
http://arxiv.org/abs/2207.07344
Autor:
Pandey, S. K.
In this note we provide important and significant observations in ring theory related to weakly tripotent rings. We provide counterexamples for the structure theorem for commutative weakly tripotent rings appeared in arXiv (2017) and Bull. Korean Mat
Externí odkaz:
http://arxiv.org/abs/2203.02274
In this paper, we study the reflexive-nilpotents-property (briefly, RNP) for Ore extensions of injective type, and more generally, skew PBW extensions. With this aim, we introduce the notions of $\Sigma$-skew CN rings and $\Sigma$-skew reflexive (RNP
Externí odkaz:
http://arxiv.org/abs/2110.14061