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.
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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.