On S-Zariski topology


YILDIZ E., ERSOY B. A. , TEKİR Ü. , KOÇ S.

COMMUNICATIONS IN ALGEBRA, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

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.