Related papers: Weakly $\sqrt{J}U$ Rings

An order is a commutative ring that as an abelian group is finitely generated and free. A commutative ring is reduced if it has no non-zero nilpotent elements. In this paper we use a new tool, namely, the fact that every reduced order has a…

Jespers and Sun conjectured that if a finite group $G$ has the property ND, i.e. for every nilpotent element $n$ in the integral group ring $\mathbb{Z}G$ and every primitive central idempotent $e \in \mathbb{Q}G$ one still has $ne \in…

In this paper, we introduce a concept of weakly principally quasi-Baer *-rings in terms of central cover. We prove that a *-rings is a principally quasi-Baer *-rings if and only if it is weakly principally quasi-Baer *-rings with unity. A…

A ring R shall be called F-noetherian if every finite subset of R is contained in a (left and right) noetherian subring of R . For example, every commutative ring is tightly F-noetherian in the sense that every finite subset of R generates…

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 this paper, we introduce and explore in-depth the notion of {\it weakly strongly 2-nil-clean rings} as a common non-trivial generalization of both strongly 2-nil-clean rings and strongly weakly nil-clean rings as defined and studied by…

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Suppose G is a finite group, and B is a block of kG with dihedral defect group D which is Morita equivalent to the principal…

In this paper, we define and study a particular case of von Neumann regular notion called a weak von Neumann regular ring. It shown that the polynomial ring $R[x]$ is weak von Neumann regular if and only if $R$ has exactly two idempotent…

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 ${}^{-1}$.…

Let $R$ be a ring and $S$ a multiplicative subset of $R$. An $R$-module $T$ is called $u$-$S$-torsion ($u$- always abbreviates uniformly) provided that $sT=0$ for some $s\in S$. The notion of $u$-$S$-exact sequences is also introduced from…

We introduce the notion of J-Armendariz rings, which are a generalization of weak Armendariz rings and investigate their properties. We show that any local ring is J-Armendariz, and then fined a local ring that is not weak Armendariz.

We say that a commutative ring R satisfies the restricted minimum (RM) condition if for all essential ideals I in R, factor R/I is an Artinian ring. We will focus on Noetherian reduced rings because in this setting known results for RM…

Given a collection $\{ G_i\}_{i=1}^d$ of finite groups and a ring $R$, we define a subring of the ring $M_n(R)$ ($n = \sum_{i=1}^d|G_i|)$ that encompasses all the individual group rings $R[G_i]$ along the diagonal blocks as $G_i$-circulant…

Let R be a ring (not necessarily with 1) and G be a finite group of automorphisms of R. The set B(R, G) of primes p such that p | |G| and R is not p-torsion free, is called the set of bad primes. When the ring is |G|-torsion free, i.e.,…

Let R be a commutative ring with identity. We investigate some ring-theoretic properties of weakly Laskerian R-modules. Our results indicate that weakly Laskerian rings behave as Noetherian ones in many respects. However, we provide some…

We call a ring $R$ NJ-symmetric if $abc\in N(R)$ implies $bac\in J(R)$ for any $a,b,c\in R$. Some classes of rings that are NJ-symmetric include left (right) quasi-duo rings, weak symmetric rings, and abelian J-clean rings. We observe that…

Given a directed graph $E$ and an associative unital ring $R$ one may define the Leavitt path algebra with coefficients in $R$, denoted by $L_R(E)$. For an arbitrary group $G$, $L_R(E)$ can be viewed as a $G$-graded ring. In this article,…

We define when a noetherian ring R is called a right ( or a left) weakly krull symmetric ring . We then prove that if R is a right ( or a left ) krull homogenous ring then R is a right ( or a left ) weakly krull symmetric ring . This result…

Let $R$ be a $G$-graded ring. In this article, we introduce two new concepts on graded rings, namely, weakly graded rings and invertible graded rings, and we discuss the relations between these concepts and several properties of graded…

In this article, we introduce the concept of weakly $I$-clean ring, for any ideal $I$ of a ring $R$. We show that, for an ideal $I$ of a ring $R$, $R$ is uniquely weakly $I$-clean if and only if $R/I$ is semi boolean and idempotents can be…