In this study, all rings are commutative with non-zero identity and all modules are considered
to be unital. Let $ M $ be a left $ R $-module. A proper submodule $ N $ of $ M $ is called an …

A Short Note on the Primary Submodules of Multiplication Modules Page 1 International Journal
of Algebra, Vol. 1, 2007, no. 8, 381 - 384 A Short Note on the Primary Submodules 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 and let M be an R-module. In this paper, we study the dual
notion of prime submodules (that is, second submodules of M). Also we introduce the dual …

Let R be a commutative ring with nonzero identity, S⊆ R be a multiplicatively closed subset
of R, and M be a unital R‐module. In this article, we introduce the concepts of S …

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}\} …

Let R be a commutative ring with identity, and M a unitary R-module M is called
multiplication if every submodule N of M is of the form MI for some ideal I of R [3]. In this work …

An R-module M is called semiprime if it is cogenerated by each of its essential submodules.
We investigate when a semiprime module M has the property that for every non-zero …

Pure and Copure Submodules 1 Introduction Page 1 International Journal of Algebra, Vol. 8,
2014, no. 14, 649 - 653 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2014.4543 …

Let R be a commutative ring with identity and M a unitary R-module, and n> 1 an integer
number. As a generalization of the concept of prime submodules, a proper submodule N of …