On S-Zariski Topology


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

Communications In Algebra, cilt.49, sa.3, ss.1212-1224, 2021 (SCI İndekslerine Giren Dergi)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Konu: 3
  • Basım Tarihi: 2021
  • Dergi Adı: Communications In Algebra
  • Sayfa Sayıları: ss.1212-1224

Özet

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.