Let R be a commutative ring with 1 and M be a (left) unitary R–module. This essay gives
generalizations for the notions prime module and some concepts related to it. We termed an …

Let R be a commutative ring with identity, and M be a left unitary R-module. In this paper, we
introduce and study type of modules namely essential weakly quasi-prime module as …

Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $
of an $ R $-module $ M $ to be weakly prime if $0\not= rm\in N $($ r\in R, m\in M $) implies …

Modules in which every proper submodule (resp. proper nonzero submodule) is prime
(called fully prime (almost fully prime)) and with some other related notions are fully …

Let R be a commutative ring with identity and M a unitary R-module. Some properties of
prime submodules of an R-module M have been discussed. In this paper, we investigate the …

Let R be an arbitrary ring and M be a right R-module. A proper submodule N of M is called
almost prime (respectively, weakly prime) if for each submodule K of M and each ideal I of R …

Let R be a commutative ring with identity and M be a unitary R-module. The notions of
associated and supported PRIME SUBMODULE s of a module are defined. Our aim is to …

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 non-zero identity. We define a proper submodule N of an R-
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …

We provide the notion of strongly semiprime submodules of a given right $ R $-module $ M
$ and describe properties of them as a generalization of completely semiprime ideals in …