The concepts of Tor-prime and Strongly Tor-prime submodules are introduced and
investigated. A proper submodule N is called Tor-prime submodule (resp. Strongly prime), if …

In this study, we introduce the concepts of $ S $-prime submodules and\$ S $%-torsion-free
modules, which are generalizations of prime submodules and torsion-free modules …

Let R be a commutative ring with identity. For t∈ N, a proper submodule N of an R-module
M is called a t-prime submodule if rm∈ N (r∈ R, m∈ M), then m∈ N or rt∈(N: RM). We …

In this paper, we introduce the classes of strongly prime and one-sided strongly prime
submodules and use these classes to characterize Noetherian modules. A finitely generated …

In this study, we introduce the concepts of S-prime submodules and S-torsion-free modules,
which are generalizations of prime submodules and torsion-free modules. Suppose S⊆ R is …

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 …

Let $ R $ be a commutative ring with identity, and let $ W $ be a unitary $ R $-module. In this
paper, we introduced the concept of a weakly semi-primary submodule as a generalization …

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 …

Abstract We present $* $-primary submodules, a generalization of the concept of primary
submodules of an $ R $-module. We show that every primary submodule of a Noetherian …

In this paper, we study S-essential submodules which are a generalization of essential
submodule of modules. Besides giving many examples and properties of S-essential …