相关论文: On SAP-rings

Based on an analogue for systems of partial isomorphisms between lower sections in a complemented modular lattice we prove that principal right ideals $aR \cong bR$ in a (von Neumann) regular ring $R$ are perspective if $aR \cap bR$ is of…

We introduce a class of rings, namely the class of left or right $p$-nil rings, for which the adjoint groups behave regularly. Every $p$-ring is close to being left or right $p$-nil in the sense that it contains a large ideal belonging to…

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…

We study the class of ADS rings and modules introduced by Fuchs. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring R such that R is ADS as a right R-module must be…

Let $R$ be a ring and $S$ a multiplicative subset of $R$. Then $R$ is called a uniformly $S$-Noetherian ($u$-$S$-Noetherian for abbreviation) ring provided there exists an element $s\in S$ such that for any ideal $I$ of $R$, $sI \subseteq…

We define the class of {\it unit uniquely clean} rings ({\it UnitUC} for short), that is a common generalization of uniquely clean rings and strongly nil clean rings. Abelian {\it UnitUC} rings are uniquely clean and {\it UnitUC} rings with…

Recently, the rings whose injective right modules are R-projective (respectively, max-projective) were investigated and studied in [2]. Such ring are called right almost-QF (respectively, max-QF). In this paper, our aim is to give some…

We give a complete description of ring isomorphisms between algebras of measurable operators affiliated with von Neumann algebras of type II$_1.$

Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings), and…

In this work we introduce a new concept, namely, $\tau_{s}$-extending modules (rings) which is torsion-theoretic analogues of extending modules and then we extend many results from extending modules to this new concept. For instance we show…

Let $R$ be a ring, a right ideal $I$ of $R$ is called small if for every proper right ideal $K$ of $R$, $I+K\neq R$. A ring $R$ is called right small injective if every homomorphism from a small right ideal to $R_{R}$ can be extended to an…

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We…

In this paper a simple right R-module S over a ring R is called hypersimple if its injective hull E(S) is cyclic, and a ring R is called right hypersimple if every simple right R-module is hypersimple. We initiate a study of these new…

A ring $R$ is called right (small) dual if every (small) right ideal of $R$ is a right annihilator. Left (small) dual rings can be defined similarly. And a ring $R$ is called (small) dual if $R$ is left and right (small) dual. It is proved…

Let $R$ be an arbitrary ring and $(-)^+=\Hom_{\mathbb{Z}}(-, \mathbb{Q}/\mathbb{Z})$ where $\mathbb{Z}$ is the ring of integers and $\mathbb{Q}$ is the ring of rational numbers, and let $\mathcal{C}$ be a subcategory of left $R$-modules and…

Given a ring R, we define its right i-profile (resp. right p-profile) to be the collection of injectivity domains (resp. projectivity domains) of its right R-modules. We study the lattice theoretic properties of these profiles and consider…

We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that the endomorphism ring of a module, endowed with the finite topology, is topologically…

In this paper all rings are commutative. We prove some new results on flat epimorphisms of rings and pointwise localizations. Especially among them, it is proved that a ring $R$ is an absolutely flat (von-Neumann regular) ring if and only…

For any ring \(R\), some characterizations are obtained for unit regular elements in a corner ring \(eRe\) in terms of unit regular elements in \(R\). \noindent {\bf Key Words}: von Neumann regular rings, unit regular rings, corner rings,…

Let $R$ be a ring and $M$ be a right $R$-module. $M$ is called neat-flat if any short exact sequence of the form $0\to K\to N\to M\to 0$ is neat-exact i.e. any homomorphism from a simple right $R$-module $S$ to $M$ can be lifted to $N$. We…