On rational extensions of a ring
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- June Irene Bowers (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Robert Bernhardt
Abstract: The purpose of this paper is to examine the rational extensions of a ring and to prove that under certain conditions the injective hull of a ring is a right self-injective, von Neumann ring. Furthermore, we shall show that the module structure of the injective hull induces the ring multiplication. In the first section of Chapter I, we define a rational extension of a module over a ring. This concept is closely related to essential extensions of modules in that every rational extension of a module is an essential extension. Several theorems that characterize rational extensions are proved. Using these theorems, we show that when MR is a right R-module with zero right singular submodule, every essential extension of MR is a rational extension.
On rational extensions of a ring
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Created on 1/1/1971
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Additional Information
- Publication
- Thesis
- Language: English
- Date: 1971
- Subjects
- Von Neumann regular rings
- Rings (Algebra)