S-Zariski Topology on S-Spectrum of Modules

YILDIZ YILMAZ E., ERSOY B. A., TEKİR Ü.

Filomat, vol.36, no.20, pp.7103-7112, 2022 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 20
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2220103y
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.7103-7112
  • Keywords: prime spectrum, S-maximal ideal, S-prime spectrum, Zariski topology
  • Yıldız Technical University Affiliated: Yes

Abstract

Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, first we give some relations between S-prime and S-maximal submodules that are generalizations of prime and maximal submodules, respectively. Then we construct a topology on the set of all S-prime submodules of M, which is generalization of prime spectrum of M. We investigate when SpecS (M) is T0 and T1-space. We also study on some continuous maps and irreducibility on SpecS (M). Moreover, we introduce the notion of S-radical of a submodule N of M and use it to show the irreducibility of S-variety VS (N).