An Essential Extension with Nonisomorphic Ring Structures II |
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| Authors: | Gary F Birkenmeier Jae Keol Park S Tariq Rizvi |
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| Institution: | 1. Department of Mathematics , University of Louisiana at Lafayette , Lafayette, Louisiana, USA gfb1127@louisiana.edu;3. Department of Mathematics , Busan National University , Busan, South Korea;4. Department of Mathematics , Ohio State University , Lima, Ohio, USA |
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| 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. |
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| Keywords: | (FI-) extending Compatible ring structure Injective hull Kasch ring Osofsky compatible ring QF-ring |
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