In this paper, we introduce the concept of sp-semisimple module. Let S be a semiradical
property, we say that a module M is sp-semisimple if for every submodule N of M, there …

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 be a unitary left R-module on associative ring with identity. A submodule of is called-
annihilator small if, where is a submodule of, implies that ann ()= 0, where ann () indicates …

Let M be a right R-module. A right R-module N is called small principally M-injective (briefly,
SP-M-injective) if, every R-homomorphism from a small and principal submodule of M to N …

Throughout this paper R represents commutative ring with identity, and M is a unitary left R-
module. The purpose of this paper is to study a new concept,(up to our knowledge), named …

Let M be a left R-module and F a submodule of M for any ring R. We call MF-semiregular if
for every x∈ M, there exists a decomposition M= A⊕ B such that A is projective, A≤ Rx and …

An R-module M is called rationally extending if each submodule of M is rational in a direct
summand of M. In this paper we study this class of modules which is contained in the class …

A submodule of an R-module M which Dauns 1 was named semiprime submodules that
they are generalized of semiprime ideals, which get big importance at last years, many …

In this paper, we introduce the notion of $ S $-$ M $-cyclic submodules, which is a
generalization of the notion of $ M $-cyclic submodules. Let $ M, N $ be right $ R $-modules …

Let M be an R-module, where R be a commutative; ring with identity. In this paper, we
defined a new kind of submodules, namely; ET-coessential and ET-Coclosed submodules of …