Through this paper R represent a commutative ring with identity and all R-modules are
unitary left R-modules. In this work we consider a generalization of the class of essential …

If R is a commutative ring with identity, then the radical of a primary ideal of R is a prime
ideal of R. We will try to study and generalize this property to modules. It is proved that if one …

Introduction. In [5] it is left as a question whether direct sums and summands of weak CS-
modules are weak CS or not. Some particular answers are given to the former question in [5 …

Let 𝑅 be a commutative ring with identity and 𝑀 is an R-module, Danus [2] was named
semiprime submodules that they are generalized of semiprime ideals, which get a big …

In [1] a Levitzki module which we here call an l-prime module was introduced. In this paper
we define and characterize l-prime submodules. Let N be a submodule of an R-module M. If …

Let M be an R-module. If for every submodule N of M, there exists an element r∈ R such that
N= rM, then we say that M is a principal ideal multiplication module. In this paper, the …

Let $ N $ be a submodule of a module $ M $ and a minimal primary decomposition of $ N $
is known‎.‎ A formula to compute Baer's lower nilradical of $ N $ is given‎.‎ The relations …

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 …

Let R be an associative ring with identity and let M be right R-module M is called μ-semi
hollow module if every finitely generated submodule of M is μ-small submodule of M The …