A proper submodule N of an R-module M is called a weakly prime [resp. a prime]
submodule, if for any elements a, b∈ R and x∈ M, the condition abx∈ N [resp. ax∈ N] …

In this paper, we introduce and study a new class of submodules which unify the concepts of
prime and primary submodules. Let M be a unital module over a commutative ring R, ϕ: L …

, E (M))= 0, where E (M) is the injective hull of M. Rational submodules have been studied
and discussed by many authors such as HH Storrer, H. Khabazian, E. Ghashghaei, A …

Let R be a commutative ring with identity and M be a unitary R-module. Various
generalizations of prime submodules have been studied. Let φ: τ (M)−→ τ (M)∪{ø} be a …

In this article, we define almost prime submodules as a new generalization of prime and
weakly prime submodules of unitary modules over a commutative ring with identity. We …

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 …

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 …

Abstract We introduced (R, S)-modules as a generalization of bimodule structures.
Moreover, we presented the ways to study primalities of (R, S)-submodules, which we called …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …