Essential Overring Extensions-Beyond the Maximal Ring of Quotients

Gary F. Birkenmeier, Jae Keol Park and S. Tariq Rizvi
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Gary F. Birkenmeier: University of Louisiana at Lafayette, Department of Mathematics
Jae Keol Park: Busan National University, Department of Mathematics
S. Tariq Rizvi: The Ohio State University at Lima, Department of Mathematics

Chapter Chapter 7 in Extensions of Rings and Modules, 2013, pp 217-266 from Springer

Abstract: Abstract The focus of this chapter is on right essential overrings of a ring which are not right rings of quotients. Osofsky’s well-known example of a finite ring whose injective hull has no compatible ring structure is considered and generalized. All possible right essential overrings of the ring in Osofsky’s example are discussed. A ring R is constructed with a module essential extension S which is not the injective hull of R. However, S is shown to have one compatible ring structure which is a QF-ring and another compatible ring structure which is not even right FI-extending. Finally, Osofsky compatibility is discussed and a class of rings whose injective hulls have distinct compatible ring structures is studied.

Keywords: Right essential overring; Compatible ring structure; Right Osofsky compatible; Morita context; Left multiplication (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-387-92716-9_7

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DOI: 10.1007/978-0-387-92716-9_7

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