On rational extensions of a ring

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
June Irene Bowers (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
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.

Additional Information

Language: English
Date: 1971
Von Neumann regular rings
Rings (Algebra)

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