In this paper we study commutative rings $ R $ whose prime ideals are direct sums of cyclic
modules. In the case $ R $ is a finite direct product of commutative local rings, the structure …

Let R be an associative ring with nonzero identity and let M be a unitary left R− module. In
this paper, we introduce the concept of weakly primary submodules of M and give some …

ON THE PRIMARY AVOIDANCE THEOREM FOR MODULES OVER COMMUTATIVE RINGS
Throughout this paper, R denotes a commutative ring with ide Page 1 ON THE PRIMARY …

Let R be a commutative ring with identity and let M be a unital left R-module. Goodearl
introduced the following concept: A submodule A of an R–module M is an y–closed …

Abstract The submodule\overline {Z}(M)=\cap {NM/N is small in its injective hull} was
introduced by Talebi and Vanaja in 2002. A ring R is said to have property (P) if\overline …

Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic
projective or faithful multiplication then M is locally either zero or isomorphic to R. We …

Let R be a commutative ring with identity and let M be an R-module. The purpose of this
paper is to introduce and investigate the submodules of an R-module M which satisfy the …

Acta Mathematica Academiae Paedagogicae Nyıregyháziensis 33 (2017), 165–173 www.emis.de/journals
ISSN 1786-0091 I-PRIME SUBM Page 1 Acta Mathematica Academiae Paedagogicae …

Let R be a commutative ring with 1≠ 0 and M a unital R-module. M is said to satisfy Property
(A) if for each finitely generated ideal J of R contained in ZR (M), there exists 0≠ m∈ M such …

ON MODULES OVER COMMUTATIVE RINGS Page 1 J. Aust. Math. Soc. 103 (2017), 341–356
doi:10.1017/S1446788717000313 ON MODULES OVER COMMUTATIVE RINGS LASZL O …