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

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let (M) be
the set of all submodules of M, and φ:(M)→(M)∪{∅} be a function. We say that a proper …

Let $ R $ be a commutative ring with identity and $ M $ be a unitary $ R $-module. Suppose
that $\phi: S (M)\rightarrow S (M)\cup\lbrace\emptyset\rbrace $ be a function where $ S (M) …

Let R be a commutative ring with non-zero identity, S⊆ R be a multiplicatively closed subset
of R and M be an R-module. A submodule N of M with (N: RM)∩ S=∅ is said to be S …

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)) …

In this work, all rings under consideration will be Supposedly to be commutative with
nonzero identity and all modules will be nonzero unital. this work we investigate some …

In this paper we introduced a definition for the primary radical of a submodule with some of
its basic properties. We also define the P-radical submodule and review some results about …

Let $ R $ be a commutative ring and let $ M $ be an $ R $-module. A submodule $ N $ of $
M $ is called a weakly primal submodule provided that the set $ P= w (N)\cup\{0\} $ forms an …

Let R be a commutative ring with identity, S a multiplicatively closed subset of R, and M be
an R-module. The aim of this article is to introduce and investigate some properties of the …