On S-Zariski Topology


Yıldız E., Ersoy B. A. , Tekir Ü., Koç S.

Communications In Algebra, vol.49, no.3, pp.1212-1224, 2021 (Journal Indexed in SCI)

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2021
  • Title of Journal : Communications In Algebra
  • Page Numbers: pp.1212-1224

Abstract

Let R be a commutative ring with nonzero identity and, SR be a multiplicatively closed subset. An ideal P of R with PS= is called an S-prime ideal if there exists an (fixed) sS and whenver abP for a,bR then either saP or sbP. In this article, we construct a topology on the set SpecS(R) of all S-prime ideals of R which is generalization of prime spectrum of R. Also, we investigate the relations between algebraic properties of R and topological properties of SpecS(R) like compactness, connectedness and irreducibility.