On S-Zariski topology

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

COMMUNICATIONS IN ALGEBRA, vol.49, no.3, pp.1212-1224, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1080/00927872.2020.1831006
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1212-1224
  • Keywords: Prime spectrum, S-Zariski topology, Zariski topology, PRIME SPECTRUM, 2ND SPECTRUM, MODULE, GRAPH
  • Yıldız Technical University Affiliated: Yes


Let R be a commutative ring with nonzero identity and, S subset of R be a multiplicatively closed subset. An ideal P of R with P boolean AND S = theta is called an S-prime ideal if there exists an (fixed) s is an element of S and whenver ab is an element of P for a, b is an element of R then either sa is an element of P or sb is an element of P. In this article, we construct a topology on the set Spec(S)(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 Spec(S)(R) like compactness, connectedness and irreducibility.