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. Various
generalizations of prime submodules have been studied. Let φ: τ (M)−→ τ (M)∪{ø} be a …

Accepted: 16/08/2022 Let R be a commutative ring with identity, and W be an R-module. In
This paper introduces the notion of 2-quasi prime submodules as a generalization of quasi …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …

We have introduced the notion of $\alpha $-prime and weakly $\alpha $-prime submodules
as a generalization of prime submodules. Some basic properties of $\alpha $-prime and …

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, $ S $ a multiplicatively closed subset of $ R $,
and $ M $ be an $ R $-module. In this paper, we study and investigate some properties of …

In this paper we investigate-primary submodules which unify prime submodules and primary
submodules. Our motivation is to extend the concept of-primary ideals into-primary …

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}\} …

This article introduces the concept of S‐semiprime submodules which are a generalization
of semiprime submodules and S‐prime submodules. Let M be a nonzero unital R‐module …