Related papers: Rings with $\Delta$-quasipolarity Property

We investigate near-ring properties that generalize nearfield properties about units. We study zero symmetric near-rings $N$ with identity with two interrelated properties: the units with zero form an additive subgroup of $(N,+)$; the units…

We survey theory developed over the past 10 years of semirings which need not be additively cancellative. The main feature is a specified ``null ideal'' $\mcA_0$ of a semiring $\mcA,$ taking the place of a zero element, which permits…

We introduce and study a class of objects that encompasses Christensen and Foxby's semidualizing modules and complexes and Kubik's quasi-dualizing modules: the class of $\mathfrak{a}$-adic semidualizing modules and complexes. We give…

Let $A$ be a finite dimensional associative $\mathbb{K}$-algebra over an algebraically closed field $\mathbb{K}$ of characteristic zero. To $A$, we can associate its basic form that is given by a quiver $Q = (Q_0, Q_1)$ with an admissible…

In this article we give a characterization of left (right) quasi-duo differential polynomial rings. In particular, we show that a differential polynomial ring is left quasi-duo if and only if it is right quasi-duo. This yields a partial…

A definition of quasi-flat left module is proposed and it is shown that any left module which is either quasi-projective or flat is quasi-flat. A characterization of local commutative rings for which each ideal is quasi-flat (resp.…

The coincidence of the set of all nilpotent elements of a ring with its prime radical has a module analogue which occurs when the zero submodule satisfies the radical formula. A ring $R$ is 2-primal if the set of all nilpotent elements of…

Let $R$ be a maximal subring of a ring $T$. In this paper we study relation between some important ideals in the ring extension $R\subseteq T$. In fact, we would like to find some relation between $Nil_*(R)$ and $Nil_*(T)$, $Nil^*(R)$ and…

Some basic properties of the ring of integers $\mathbb{Z}$ are extended to entire rings. In particular, arithmetic in entire principal rings is very similar than arithmetic in the ring of integers $\mathbb{Z}$. These arithmetic properties…

As a generalisation of Graham and Lehrer's cellular algebras, affine cellular algebras have been introduced in [12] in order to treat affine versions of diagram algebras like affine Hecke algebras of type A and affine Temperley-Lieb…

We introduce noncommutative rings with $DK$-property (Dubrovin-Komarnytsky's property) and investigate elementary divisor rings with such property. Mostly we pay attention to these kinds of noncommutative rings which have stable range $1$.…

We give three families of parabolic rational maps and show that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetrically equivalent to the Julia set of one map in these families for suitable…

We introduce primitive hyperideals of a hyperring R and show relations with R itself, and with maximal and prime hyperideals of R. We endow a Jacobson topology on the set of primitive hyperideals of R and study topological properties of the…

A ring with an involution * is called strongly $J$-*-clean if every element is a sum of a projection and an element of the Jacobson radical that commute. In this article, we prove several results characterizing this class of rings. It is…

In the present paper, as a generalization of the classical periodic rings, we explore those rings whose elements are additively generated by two (or more) periodic elements by calling them additively periodic. We prove that, in some major…

In order to find a suitable expression of an arbitrary square matrix over an arbitrary finite commutative ring, we prove that every such a matrix is always representable as a sum of a potent matrix and a nilpotent matrix of order at most…

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. By $J(R),$ we denote the Jacobson radical of $R$. The purpose of this paper is to introduce the concept of weakly $J$-submodules generalizing $J$-submodules. We…

Let $G$ be a compact $p$-adic analytic group. We recall the well-understood finite radical $\Delta^+$ and FC-centre $\Delta$, and introduce a $p$-adic analogue of Roseblade's subgroup $\mathrm{nio}(G)$, the unique largest orbitally sound…

A ring $R$ is periodic provided that for any $a\ in R$ there exist distinct elements $m,n \in {\Bbb N}$ such that $a^m=a^n$. We shall prove that periodicity is inherited by a type of generalized matrix rings.We define strongly periodic…

We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…