Zariski-Like Topology on S-Quasi-Primary Ideals of a Commutative Ring. (4th November 2022)

• Record Type: Journal Article
• Authors: Al Subaiei, Bana; Jarboui, Noômen
• Other Names: Farshadifar Faranak Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-11-04
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/9177320
• Languages: English
• ISSNs: 2314-4629

Abstract

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.