Let R be a commutative ring with non-zero identity, S⊆ R a multiplicatively closed subset of
R and M a unital R-module. In this paper, we introduce the concepts of S-almost semiprime …

This article introduces the concept of S‐semiprime submodules which are a generalization
of semiprime submodules and S‐prime submodules. Let M be a nonzero unital R‐module …

In this work, we give generalizations for the concepts essential submodule and uniform
module. We call an R-submodule N of M semi-essential if N∩ P≠ 0 for each nonzero prime …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …

Let R be a commutative ring with 1 ≠ 0 1≠ 0 and M be a nonzero unital R-module. Recall
that a proper submodule N of M is called a semiprimary submodule of M if whenever rm ∈ N …

Let S be a semiring. An S-semimodule M is called a multiplication semimodule if for each
subsemimodule N of M there exists an ideal I of S such that N= IM. In this paper we …

Let R be an arbitrary ring, M a rightR-module and S= EndR (M), the endomorphism ring of M.
A proper fully invariant submodule X of M is called a prime submodule of M if for any ideal I …

In this paper, we introduce and study some new generalizations of second submodules via a
function φ on the set of all submodules of a module. Let R be a ring with non-zero identity, M …