The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …

In this article, we introduce the notion of strongly π-regular module which is a generalization
of von Neumann regular module in the sense [13]. Let A be a commutative ring with 1≠ 0 …

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 …

In this article, we introduce the notion of strongly 𝜋-regular module which is a generalization
of von Neumann regular module in the sense [13]. Let 𝐴 be a commutative ring with 1≠ 0 …

An $ R $-module $ M $ is called torsion-free, if $ rx= 0$ for $ r\in R $ and $ x\in M $ implies
that $ r= 0$ or $ x= 0$. In this paper, we introduce the notions semi torsion-free modules and …

Let R be a commutative ring with 1 and M be a (left) unitary R–module. This essay gives
generalizations for the notions prime module and some concepts related to it. We termed an …

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 M be a left R-module. Then a proper submodule P of M is called weakly prime
submodule if for any ideals A and B of R and any submodule N of M such that ABN⊆ P, we …

Modules over strongly prime rings Page 1 Journal of Algebra and Its Applications Vol. 14, No. 5
(2015) 1550076 (9 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219498815500760 …

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 …