ABSTRACT A new notion which is called weakly stable module is introduced in this article. It
is a nontrivial generalization of the modules with endomorphism rings having stable range …

Let R be a commutative ring with identity and M be a unitary R-module. By J (R), we denote
the Jacobson radical of R. The purpose of this paper is to introduce the concept of weakly J …

It is shown that if every prime ideal minimal over an ideal I is finitely generated, then there
are only finitely many prime left ideals minimal over I. This immedeately generalizes Cohen's …

ON GRADED SECOND MODULES Page 1 TAMKANG JOURNAL OF MATHEMATICS Volume
43, Number 4, 499-505, Winter 2012 doi:10.5556/j.tkjm.43.2012.499-505 - + +- - - - - Available …

In this paper we extend several results known for reduced rings to reduced modules. We
prove that for a semiprime module or a module with zero Jacobson radical, the concepts of …

arXiv:1604.07656v1 [math.AC] 26 Apr 2016 Page 1 arXiv:1604.07656v1 [math.AC] 26 Apr 2016
ON (k, n)-CLOSED SUBMODULES ECE YETKIN CELIKEL Abstract. Let R be a commutative ring …

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 …

Throughout this paper, let R be a commutative ring (with identity) and M be a unital R-
module. A proper submodule N of M with N: RM= p is said to be prime or p-prime (pa prime …

In this article, we introduce the notion of strongly??-regular module which is a
generalization_x000D_ of von Neumann regular module in the sense [13]. Let?? be a …