Related papers: Rings with 2-$\Delta$U property

By a ring we always mean a commutative ring with identity. It is well known that maximal spectrum of $C(X)$, $C^*(X)$ and any intermediate subrings between $C(X)$ and $C^* (X)$ are homeomorphic and homeomorphic with $\beta X$, the…

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…

Let $M$ be a module. A {\em $\delta$-cover} of $M$ is an epimorphism from a module $F$ onto $M$ with a $\delta$-small kernel. A $\delta$-cover is said to be a {\em flat $\delta$-cover} in case $F$ is a flat module. In the present paper, we…

We define and examine the class of {\it strongly \( J^{\#} \)-clean rings} consisting of those rings $R$ such that each element of $R$ is the sum of an idempotent from $R$ and an element from $J^{\#}(R)$ that commute with each other. More…

In this paper we seek to determine the Jacobson radical of certain algebras based on semigroups, and in particular on the semigroups $(\beta S, \Box)$, where $S$ is a cancellative, countable, abelian semigroup and $\beta S$ is its…

A left and right noetherian semiperfect ring R is known to be indecomposable if and only if its factor by the second power of Jacobson radical is. This characterisation is used to study simple R-modules in terms of their Ext groups. It is…

In this paper, we introduce a new class of rings whose elements are a sum of a central element and a nilpotent element, namely, a ring $R$ is called$CN$ if each element $a$ of $R$ has a decomposition $a = c + n$ where $c$ is central and $n$…

Let $K$ be a 2-torsion free ring with identity and $R_{n}(K,J)$ be the ring of all $n\times n$ matrices over $K$ such that the entries on and above the main diagonal are elements of an ideal $J$ of $K.$ We describe all Jordan derivations of…

Given a t.u.p.-semigroup (two unique product semigroup) $X$, we show if $R$ is an $X$-graded ring then both its nilradical and Jacobson radical are homogeneous. This partially answers questions of Smoktunowicz and Jespers.

We consider the group theoretical properties of R--R scalars of string theories in the low-energy supergravity limit and relate them to the solvable Lie subalgebra $\IG_s\subset U$ of the U--duality algebra that generates the scalar…

Let $R$ be a commutative ring with identity. In this paper, we introduce the concept of quasi $J$-ideal which is a generalization of $J$-ideal. A proper ideal of $R$ is called a quasi $J$-ideal if its radical is a $J$-ideal. Many…

We search for principal ideals. As a sample, let $R$ be a strongly-normal, almost-factorial, and complete-intersection local ring with a prime ideal $P$ of height one. If $depth(R/ P)\geq dim R-2$, we show $P$ is principal. As an immediate…

A commutative ring $R$ is stable provided every ideal of $R$ containing a nonzerodivisor is projective as a module over its ring of endomorphisms. The class of stable rings includes the one-dimensional local Cohen-Macaulay rings of…

A ring $R$ is called a J-regular ring if R/J(R) is von Neumann regular, where J(R) is the Jacobson radical of R. It is proved that if R is J-regular, then (i) R is right n-injective if and only if every homomorphism from an $n$-generated…

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…

This paper is devoted to the units of integral group rings of cyclic $2$-groups of small orders, namely, the orders of $2^n$ for $n<8$. Immediately we should note the issues our consideration describe in the introduction in more detail.…

Let $R$ be either the ring of Lipschitz quaternions, or the ring of Hurwitz quaternions. Then, $R$ is a subring of the division ring $\mathbb{D}$ of rational quaternions. For $S \subseteq R$, we study the collection $\rm{Int}(S,R) = \{f \in…

Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that…

A method is proposed and tested for the analysis of Delta I=2 staggering observed in nuclear rotational bands. We examine six super- and hyper-deformed bands, among which that of 149Gd and possibly of 147Gd seem to exhibit real staggering.…

A rank-$r$ integer matrix $A$ is $\Delta$-modular if the determinant of each $r \times r$ submatrix has absolute value at most $\Delta$. The class of $1$-modular, or unimodular, matrices is of fundamental significance in both integer…