Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of
this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary …

In this paper, we introduce and study a new class of submodules which unify the concepts of
prime and primary submodules. Let M be a unital module over a commutative ring R, ϕ: L …

Let R be a commutative ring with identity and M be a unitary R-module. Let ϕ: S (M)→ S
(M)∪{∅} be a function, where S (M) is the set of submodules of M. Suppose n≥ 2 is a …

Let R be a commutative ring with identity and M be a unitary R-module. Various
generalizations of prime submodules have been studied. Let φ: τ (M)−→ τ (M)∪{ø} be a …

Let $ R $ be a commutative ring and $ M $ be an $ R $-module. In this paper, we investigate
some properties of 2-absorbing submodules of $ M $. It is shown that $ N $ is a 2-absorbing …

Let R be a commutative ring with identity and M be a unitary R-module. A proper submodule
N of M is 2− absorbing if r1, r2, r3∈ R, m∈ M with r1r2r3m∈ M implies r1r2m∈ N or …

All rings in this article are commutative rings with identity, and all 𝑅-modules are left unitary
𝑅-modules. A proper submodule 𝐸 of an 𝑅-module 𝑋 is called 2-absorbing if whenever …

Throughout this paper, $ R $ is an associative ring (not necessarily commutative) with
identity and $ M $ is a right $ R $-module with unitary. In this paper, we introduce a new …

In this paper, we study the concepts of n-absorbing and weakly n-absorbing submodules of
modules over a commutative ring with non-zero unity which is a generalization of prime and …

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let S (M)
be the set of all submodules of M and ${\phi}: S (M){\rightarrow} S (M){\cup}\{{\emptyset}\} …