Zariski-Like Topology on S-Quasi-Primary Ideals of a Commutative Ring

Author:

Al Subaiei Bana1ORCID,Jarboui Noômen2

Affiliation:

1. Department of Mathematics and Statistics, College of Science, King Faisal University, P. O. Box 400, Al-Ahsa 31982, Saudi Arabia

2. Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, P. O. Box 1171, Route de Soukra, Sfax 3038, Tunisia

Abstract

Let R be a commutative ring with nonzero identity and, S R be a multiplicatively closed subset. An ideal P of R is called an S -quasi-primary ideal if P S = and there exists an (fixed) s S and whenever a b P for a , b R then either s a P or s b P . In this paper, we construct a topology on the set Q Prim S R of all S -quasi-primary ideals of R which is a generalization of the S -prime spectrum of R . Also, we investigate the relations between algebraic properties of R and topological properties of Q Prim S R like compactness, connectedness and irreducibility.

Funder

Deanship of Scientific Research, King Faisal University

Publisher

Hindawi Limited

Subject

General Mathematics

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