On ring extensions satisfying the star-hash property

Abstract

Let be a ring extension, and let be a strict star operation on the extension The extension is said to satisfy the ⋆-hash property if for any two distinct subsets and of where is the set of all S-regular ⋆-maximal ideals of R. We study ring extensions satisfying the star-hash property. Special attention is given to the case of Prüfer extensions.