On S-Zariski topology - Yildiz, Eda; Ersoy, Bayram Ali; Tekir, Unsal; Koc, Suat (TAYLOR & FRANCIS INC, 2021)
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.
Keywords: Prime spectrum; S-Zariski topology; Zariski topology; 2ND SPECTRUM; MODULE; GRAPH; Mathematics