S-Zariski Topology on S-Spectrum of Modules

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

Filomat, cilt.36, sa.20, ss.7103-7112, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 20
  • Basım Tarihi: 2022
  • Doi Numarası: 10.2298/fil2220103y
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.7103-7112
  • Anahtar Kelimeler: prime spectrum, S-maximal ideal, S-prime spectrum, Zariski topology
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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).