S-Zariski Topology on S-Spectrum of Modules

Yıldız E., Ersoy B. A., Tekir Ü.

FILOMAT, vol.36, no.20, pp.7103-7112, 2022 (SCI-Expanded)

  • 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
  • Yıldız Technical University Affiliated: Yes


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).