Zariski-Like Topology on S-Quasi-Primary Ideals of a Commutative Ring. (4th November 2022) - Al Subaiei, Bana; Jarboui, Noômen
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.