Let $ R $ be a commutative ring with identity, and\(U_ {R}\) be an $ R $-module, with\(E=
End (U_ {R})\). In this work we consider a generalization of class small essential …

Let $ R $ be a ring and $ M $ be a unital left $ R $-module. We define $\mu^{\ast} $-essential
extension relation on the set of submodules of $ M $ and investigate its properties …

Let $ R $ be a commutative ring with identity, and let $ W $ be a unitary $ R $-module. In this
paper, we introduced the concept of a weakly semi-primary submodule as a generalization …

Let\(L\) be a left module over a ring\(\text {\S}\) with identity. In this paper, the concept of
primary isolated submodules is introduced. We look for relations between this class of …

In this paper, we study S-essential submodules which are a generalization of essential
submodule of modules. Besides giving many examples and properties of S-essential …

‌Let $ R $ be a commutative ring with identity ‌ $ ‌1\neq 0‌ $ ‌and $ M $ a nonzero unital $ R $-
module‌. ‌In this paper‌, ‌we introduce a new notion of submodules in $ M $ ‌, ‌namely $ T …

Let S be a commutative ring with identity, let A be an until (left) S-module. In this paper, we
study the concepts: essential prime sub-modules as a generalization of prime sub-modules …

This paper is concerned with S-co-m modules which are a generalization of co-m modules.
In section 2, we introduce the S-small and S-essential submodules of a unitary $ R $-module …

In this work, every ring has unity and every module is unital left module. Let M be an R-
module and N be a submodule of M. If L= 0 for every L≪ g M with N∩ L= 0, then N is called …

In this paper we Proved other properties of essential and complement submodules to an
arbitrary submodule of an R-module M. We prove that for a family {Mα} α∊ ʌ of modules. If …