S-Strongly 0-Dimentional Rings

Abstract

Let R be a commutative ring with identity, and let S be a not necessarily saturated multiplicative subset of R. We introduce the notions of strongly S-prime ideals and S-strongly 0-dimensional rings as S-analogues of strongly prime ideals and strongly 0-dimensional rings. We establish fundamental properties of these structures and provide characterizations supported by illustrative examples. We further obtain new criteria for S-Artinian rings, showing that such rings are always S-strongly 0-dimensional and finitely S-cogenerated. Finally, we examine several equivalent conditions under which a ring is compactly S-packed.