In this article, we introduce new classes of submodules called $ r $-submodule and special
$ r $-submodule, which are two different generalizations of $ r $-ideals. Let $ M $ be an $ R …

Let $\Omega $ be a group with identity $ e $, $\Gamma $ be a $\Omega $-graded
commutative ring and $\Im $ a graded $\Gamma $-module. In this article, we introduce the …

An R‐module A is called GF‐regular if, for each a∈ A and r∈ R, there exist t∈ R and a
positive integer n such that rntrna= rna. We proved that each unitary R‐module A contains a …

In this note, we define the antisimple radical, A (M), of a Γ-ring M. A (M) is shown to be a
special radical, and two characterizations of antisimple rings due to Szész are extended to Γ …

The aim of this note is to study the structure of a $\Gamma $-ring (not in the sense of
Nobusawa) with minimum conditions. By ring theoretical techniques, we obtain various …

ساهرة ياسين رياضيات P3 Page 1 Journal of Al-Nahrain University Vol.14 (1), March, 2011,
pp.157-160 Science 1 (M) - Supplemented Modules Sahira M.Yaseen and Zainab T.Salman …

SOME RESULTS ON GAMMA NEAR-RINGS Yong Uk Cho* 1. Introduction Throughout this
paper M stands for a Γ-near-ring. For basic defi- Page 1 JOURNAL OF THE CHUNGCHEONG …

Let R be a ring and M a right R-module. M is called Rad-⊕-s-module if every submodule of
M has a Rad-supplement that is a direct summand of M, and M is called completely Rad-⊕-s …

Let R be an associative ring with identity and let M be a unital left R-module. E. Akalan, G.
Birkenmeier and A. Tercan introduced the following concept. An R-module M is called a 𝒢 …

We investigate some properties of n-submodules. More precisely, we find a necessary and
sufficient condition for every proper submodule of a module to be an n-submodule. Also, we …