Let R be a commutative ring with identity and let M be a unital left R-module. Goodearl
introduced the following concept: A submodule A of an R–module M is an y–closed …

Let be a unitary left R-module on associative ring with identity. A submodule of is called-
annihilator small if, where is a submodule of, implies that ann ()= 0, where ann () indicates …

The purpose of this paper is to introduce new concepts in a module over a ring, the first one
is called e*-small essential submodule, which is a generalization of the small submodule …

Let R be associative ring with identity and let M be unitary left R-module. A submodule N of
M is called, T-small in M denoted by N≪ TM, in case for any submodule X⊆ M, T⊆ N+ X …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …

In this paper, we give a generalization for weakly primary submodules called $ I $-primary
submodule and we study some properties of it. We give some characterizations of $ I …

This article introduces the concept of S-2-absorbing primary submodule as a generalization
of 2-absorbing primary submodule. Let S be a multiplicatively closed subset of a ring R and …

Let $ R $ be a commutative ring with identity and let $ M $ be an R-module. This study
presents the nearly locally hollow module that's a strong form of a hollow module. We …

Let be a unitary left R-module on associative ring with identity. Asubmodule of is called-
annihilator small if, where is asubmodule of, implies that ann ()= 0, where ann () indicates …

A proper submodule N of an R-module M is called a weakly prime [resp. a prime]
submodule, if for any elements a, b∈ R and x∈ M, the condition abx∈ N [resp. ax∈ N] …