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Original Articles

On the Finiteness of Noetherian Rings with Finitely Many Regular Elements

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Pages 2869-2870 | Received 24 Dec 2012, Published online: 13 Mar 2014
 

Abstract

Let R be a left Noetherian ring and ZD(R) be the set of all zero-divisors of R. In this paper, it is shown that if R \ ZD(R) is finite, then R is finite.

2010 Mathematics Subject Classification:

ACKNOWLEDGMENTS

The authors are deeply grateful to Professor Donald S. Passman for the proof of Lemma 2. The research of the first author was in part supported by a grant from IPM (No. 91050212).

Notes

Communicated by M. Bresar.

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