For any module M over a commutative ring R, Spec_ R (M) S pec R (M)(resp. Max_ R (M) M
ax R (M)) of M is the collection of all prime (resp. maximal) submodules. In this article, we …

Let R be a commutative ring and M an R-module. Let Spec^ s (M) S pecs (M) be the
collection of all second submodules of M. In this article, we consider a new topology on …

ON MAX-INJECTIVE MODULES 1. Introduction Throughout this article, R denotes a
commutative ring with non zero identity and all mo Page 1 Journal of Algebra and related …

Let R be a commutative ring and let M be a top R-module. In this article, we investigate some
properties of a new class of modules, called strongly top modules. Studying of this family …

Let R be a commutative ring with identity and let M be an R-module. A proper submodule P
of M is called a classical prime submodule if abm∈ P for a, b∈ R, and m∈ M, implies that …

Let R be a commutative ring with identity and Spec^ s (M) Spec s (M) denote the set all
second submodules of an R-module M. In this paper, we investigate various properties of …

Throughout this paper, all rings are associative rings with an identity and all modules are
unitary right R-modules. Let M be a right R-module and S= End R (M), its endomorphism …

The subject of this paper is the Zariski topology on a multiplication module $ M $ over a
commutative ring $ R $. We find a characterization for the radical submodule $ rad_ {M}(0) …

Inspired by the interplay between the Zariski topology defined on the prime spectrum of a
commutative ring R and the ring theoretic properties of R in [3, 8, 18, 23, 25], we introduce in …

Let M be a left R-module. The set of all prime submodules of M is called the spectrum of M
and denoted by Spec (RM), and that of all prime ideals of R is denoted by Spec (R). For …