Different and distinct notions of regularity for modules exist in the literature. When these
notions are restricted to commutative rings, they all coincide with the well-known von …

In this article, we introduce the notion of strongly 𝜋-regular module which is a generalization
of von Neumann regular module in the sense [13]. Let 𝐴 be a commutative ring with 1≠ 0 …

We study modules whose endomorphism rings possess various forms of von Neumann
regularity. We characterize these “regularity” properties for several classes of modules …

Results gotten for a module M over a commutative ring have been broadened to module
over a ring which is not necessarily commutative. It has been indicated that an R-module M …

In this paper, we introduce $\phi $-1-absorbing prime ideals in commutative rings. Let $ R $
be a commutative ring with a nonzero identity $1\neq0 $ and $\phi:\mathcal {I}(R)\rightarrow …

In this article, we introduce the notion of M-coidempotent elements of a ring and investigate
their connections with fully coidempotent modules, fully copure modules and vn-regular …

This paper aims to introduce a new class of submodules, called (m, n)-semiprime
submodule, which is a generalization of semiprime submodule. Let M be a unital A-module …

In this paper, we introduce ϕ ϕ-1-absorbing prime ideals in commutative rings. Let R be a
commutative ring with a nonzero identity 1 ≠ 0 1≠ 0 and ϕ: I (R) → I (R) ∪ {∅\} ϕ: I (R)→ I …

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let $ R
$ be a commutative ring with a nonzero identity. A proper ideal $ P $ of $ R $ is said to be a …

In this article, we introduce the notion of strongly π-regular module which is a generalization
of von Neumann regular module in the sense [13]. Let A be a commutative ring with 1≠ 0 …