In this article, we call a ring R right generalized semiregular if for any a∈ R there exist two
left ideals P, L of R such that lr (a)= P⊕ L, where P⊆ Ra and Ra∩ L is small in R. The class …

A ring R is defined to be semiabelian if every idempotent of R is either right semicentral or
left semicentral. It is proved that the set N (R) of nilpotent elements in a π‐regular ring R is …

Abstract top A ring R is defined to be left almost Abelian if ae= 0 implies a R e= 0 for a∈ N
(R) and e∈ E (R), where E (R) and N (R) stand respectively for the set of idempotents and …

For a ring R and a right R-module M, a submodule N of M is said to be δ-small in M if,
whenever N+ X= M with M/X singular, we have X= M. If there exists an epimorphism p: P→ M …

1. A ring R is regular if for every ae R there exists an xe R such that axa= a. A regular ring
with an involution* is called*-regular if xx*= 0 implies x= 0. In this note, we study*-regular …

A ring R is π-regular if for every a in R, there is a positive integer n such that an R is
generated by an idempotent. In this paper, we introduce the notion of π-*-regular rings …

ABSTRACT A∗-ring R is called∗-regular if every principal one-sided ideal of R is generated
by a projection. The paper is devoted to a study of∗-regularity of∗-rings. Basic properties …

For a ring R, denote by the circle multiplication of R defined by ab ¼ a ş b À ab for any a, b 2
R. Then ğR, Ş is a semigroup with the identity 0, called the adjoint or circle semigroup of R …

All rings are assumed to be associative and (except for nil-rings and for some stipulated
cases) to have nonzero identity elements. A ring A is said to be regular if for every element a …

In this paper, we investigate some properties of rings whose simple (singular) right R−
modules are AP-injective. It is proved that an MERT ring R is von Neumann regular if and …