An essential extension with nonisomorphic ring structures II

作者：Birkenmeier Gary F^*; Park Jae Keol; Rizvi S Tariq

来源：Communications in Algebra, 2007, 35(12): 3986-4004.

DOI：10.1080/00927870701509552

• (FI-) extending
• compatible ring structure
• injective hull
• Kasch ring
• Osofsky compatible ring
• QF-ring

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.

• 出版日期2007