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

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 ab∈P for a,b∈R then either sa∈P or sb∈P. In this paper, we construct a topology on the set QPrimSR 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 QPrimSR like compactness, connectedness and irreducibility.