An Essential Extension with Nonisomorphic Ring Structures II

Abstract

We construct a ring R with R = Q(R), the maximal right ring of quotients of R, and a right R-module essential extension S R of R R such that S has several distinct isomorphism classes of compatible ring structures. It is shown that under one class of these compatible ring structures, the ring S is not a QF-ring (in fact S is not even a right FI-extending ring), while under all other remaining classes of the ring structures, the ring S is QF. We demonstrate our results by an application to a finite ring.