Related papers: A note on semicentral Idempotents

In order to study the properties of SEP elements, we propose the concepts of one sided a_idempotent and one sided a_equivalent. Under the condition that an element in a ring is both group invertible and MP_invertible, some equivalent…

In this paper, we explore the nature of central idempotents of Schur rings over finite groups. We introduce the concept of a lattice Schur ring and explore properties of these kinds of Schur rings. In particular, the primitive, central…

We show that every finite ring has a partition, where each block corresponds to one idempotent. Remarkably, this partition provides a way to \emph{lift} a wide variety of special elements such as idempotents, nilpotents, unipotents, roots…

The 5-element Brandt semigroup $B_2$ admits the structure of a naturally semilattice-ordered inverse semigroup, thus becoming an additively idempotent semiring with the operation of taking greatest lower bounds as the semiring addition. For…

For every group $G$, the set $\mathcal{P}(G)$ of its subsets forms a semiring under set-theoretical union $\cup$ and element-wise multiplication $\cdot$ and forms an involution semigroup under $\cdot$ and element-wise inversion ${}^{-1}$.…

This article investigates the properties of Dedekind superrings, invertible supermodules and projective supermodules within the $\mathbb{Z}_2$-graded framework. Rather than treating these entities as specialized instances of general…

Armendariz and semicommutative rings are generalizations of reduced rings. In \cite{IN}, I.N. Herstein introduced the notion of a hypercenter of a ring to generalize the center subclass. For a ring $R$, an element $a \in R$ is called…

It was conjectured at the end of the book "Representation theory of Artin algebras" by M. Auslander, I. Reiten and S. Smalo that an Artin algebra with the property that its finitely generated indecomposable modules are up to isomorphism…

We study idempotent analogs of topological tensor products in the sense of A. Grothendieck. The basic concepts and results are simulated on the algebraic level. This is one of a series of papers on idempotent functional analysis.

Let $S$ be a multiplicatively idempotent congruence-simple semiring. We show that $|S|=2$ if $S$ has a multiplicatively absorbing element. We also prove that if $S$ is finite then either $|S|=2$ or $S\cong End(L)$ or $S^{op}\cong End(L)$…

In this paper, we introduce a class of rings in which every nilpotent element is central. This class of rings generalizes so-called reduced rings. A ring $R$ is called {\it central reduced} if every nilpotent element of $R$ is central. For…

We provide a complete characterization of the equivariant commutative ring structures of all the factors in the idempotent splitting of the G-equivariant sphere spectrum, including their Hill-Hopkins-Ravenel norms, where G is any finite…

We study the finite basis problem for 4-element additively idempotent semirings whose additive reducts are semilattices of height 1. Up to isomorphism, there are 58 such algebras. We show that 49 of them are finitely based and the remaining…

In this article we introduce the study of fuzzy semihyperrings and fuzzy R-semihypermodules, where R is a semihyperrings and R-semihypermodules are represntations of R. In particular, semihyperrings all of whose hyperideals are idempotent,…

We prove that the variety V of commutative multiplicatively idempotent semirings satisfying x + y + xyz = x + y is generated by single semirings. Moreover, we describe a normal form system for terms in V and we show that the word problem in…

A ring $R$ with center $C$ is said to be\textit{centrally essential} if the module $R_C$ is an essential extension of the module $C_C$. We describe centrally essential exterior algebras of finitely generated free modules over not necessary…

This paper, we consider some properties of rings via q-potent and periodic elements. In this paper we give some results of rings in which every element is a sum of an idempotent and a q-potent that commute; periodic rings and k-potent…

In this paper, the notion of quasi-pseudo injectivity relative to a class of submodules, namely, quasi-pseudo principally injective has been studied. This notion is closed under direct summands. Several properties and characterizations have…

Let G be an algebraic group over an algebraically closed field of positive characteristic such that its neutral connected component is a unipotent group. We consider a certain class of closed idempotents in the braided monoidal category…

This paper provides answers to several open problems about equational theories of idempotent semifields. In particular, it is proved that (i) no equational theory of a non-trivial class of idempotent semifields has a finite basis; (ii)…