This paper is motivated by the results in [6]. We study some properties of strongly irreducible
submodules of a module. In fact, our objective is to investigate strongly irreducible modules …

Strongly irreducible submodules of modules are defined as follows: A submodule N of an R–
module M is said to be strongly irreducible if for submodules L and K of M, the inclusion L∩ …

In this note all are commutative rings with identity and all modules are unital. Let R be a ring.
An R-module M is called a multiplication module if for every submodule N of M there esists …

Let $ R $ be a commutative ring with identity and $ M $ be a unitary $ R $-module. A
submodule $ N $ of $ M $ is called a dense submodule if ${\rm {Hom}} _R (M/N, E_R (M)) …

Let R be a commutative ring with identity and M a unital R-module. The module M is said to
be a multiplication module provided for each submodule N of M there exists an ideal I of R …

Let R be a commutative ring with identity and let M be an R-module. Then M is called a
multiplication module if for every submodule N of M there exists an ideal I of R such that N …

In this paper we study weakly prime submodules of a module over a commutative ring with
identity. First, a number of results concerning weakly prime submodules are given. Second …

\S 0. Introduction. The main purpose of this paper is to extend some results on completely
reducible modules to quasi-injective modules by replacing “irreducible submodules” with …

Let R be a commutative ring with 1, and K the total quotient ring of R. If I is any ideal in R,
then I-'=(x EK 1 x I c R). If 11-I= R, then I is said to be an invertible ideal,[a. Let M be any …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …