Let R be a commutative ring with identity. We will say that an R-module M has Nakayama
property, if IM= M, where I is an ideal of R, implies that there exists a∈ R such that aM= 0 …

As a generalization of Nakayama's lemma, we know the concept of small submodules and
many authors have studied those submodules in projectives [11,[3],[7] and [8]. In [21 and [41 …

In 1971, Koehler proved a structure theorem for quasi-projective modules over right perfect
rings by using results of Wu–Jans. Later Mohamed–Singh studied discrete modules over …

Let R be a Noetherian ring and let C be a semidualizing R-module. In this paper, by using
the classes 𝒫 C and ℐ C, we extend the notions of perfect and coperfect modules introduced …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …

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 Let X=(M: Z"(M)= 0) and X*=(M: Q< P< M, P/Q e X implies P/Q= 0) be classes of R-
modules. In this note we study the structure of rings R over which every module M has a …

Camillo [31 and Faith [61 called a ring R a right max ring if every non-zero right R-module
has a maximal submodule. The class of right max rings includes right perfect rings (Bass [2]) …

Let R be a ring and M a right R‐module. It is shown that (1) δ (M) is Noetherian if and only if
M satisfies ACC on δ‐small submodules;(2) δ (M) is Artinian if and only if M satisfies DCC on …

An interesting result, obtaining by some theorems of Asano, Köthe and Warfield, states
that:“for a commutative ring R, every module is a direct sum of uniform modules if and only if …