Let M be a right R-module. Define Z (N)(8 M (N)) to be the set of elements ne N for any R-
module N in a [M] such that nR is an M-small (respectively 8-M-small) modüle. In this note it …

Let $ R $ be a graded commutative ring with non-zero unity $1 $ and $ M $ be a graded
unitary $ R $-module. Let $ GS (M) $ be the set of all graded $ R $-submodules of $ M $ and …

Let R be a commutative ring with identity and M be an R-module. A proper submodule N of
M is called an n-submodule if for a∈ R, m∈ M, am∈ N with a∈√ AnnR (M), implies m∈ N …

Introduction. Throughout the paper, M stands for a F-ring, as defined by Barnes [1]. We shall
utilize thestandard notations and definitions in Barnes [1] and Hsu [2]. In [2] Hsu has …

(R, S)-SUBMODULES Page 1 ON THE (m, n)-JOINTLY PRIME RADICAL (R, S)-SUBMODULES
Thawatchai Khumprapussorn Department of Mathematics Faculty of Science King …

Let R be a commutative ring with identity and M be an R-module. Let Z2 (M) be the second
singular submodule of M. In this research we introduce the concept of Goldie Pure Rickart …

Let R be a ring and M a right R-module. M is called--δ⊕ supplemented, if every submodule
of M has a-δ supplemented that is a direct summand of M. In this paper, several properties of …

In this paper, we introduce and investigate some properties of $\phi $-$\delta $-$ S $-
primary submodules, which is a generalization of the $\phi $-$\delta $-primary submodules …

Let R be a commutative ring with identity and M be an R-module. In this paper we
introducethe dual concepts of Pure Rickart modules and Pure𝜋-Rickart modulesas a …