Links ore sets,and classical localizations |
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Authors: | Mark L. Teply |
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Affiliation: | Department of Mathematical Sciences , University of Wisconsin-Milwaukee , Milwaukee, WI, 53201, USA |
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Abstract: | The notion of a simple ring DGderived from a group ring KG is introduced in case K is a field and G is an infinite residually finite group. The close link between DGand KG is exploited in both directions: first, for a simple proof of the Kaplansky's conjecture concerning direct finiteness of KG. Second, to show that DGprovides counter-examples to some conjectures dealing with von Neumann regular rings and the rings all of whose one-sided ideals are generated by idempotents. |
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Keywords: | group ring von Neumann regular ring tensor product. 1980 Mathematics subject classifications: 16S34, 16E50. |
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