On S-Integral Domains and S-Version of Krull Intersection Theorem

Abstract

Let S ⊆ R be a multiplicative closed set of a ring R. We extend several results of integral domains to S-version and establish the S-Krull intersection theorem. We also show that if R is an S-field, then the localization of R with respect to S is an ϕ(S)-field, where ϕ(S) is a multiplicative closed subset of S ^{-1}R, and prove the converse under an additional condition. As a consequence, we show that every finite S-integral domain is an S-field. Also, we provide several examples to illustrate the significance of our findings.