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.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors thank the referee and Professor B. L. Osofsky for their helpful suggestions and comments for improving the results of this article. Also the authors are grateful for the support they received from the Mathematics Research Institute, Columbus and for the kind hospitality and support of Busan National University, the Ohio State University at Lima, and the University of Louisiana at Lafayette.
Notes
Communicated by T. Albu.