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Locally Finite Ring Varieties
Awad A. Iskander
Proceedings of the American Mathematical Society
Vol. 50, No. 1 (Jul., 1975), pp. 28-32
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040508
Page Count: 5
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Necessary and sufficient conditions are given for a variety of associative rings to be locally finite. These conditions are utilized to show that a variety is generated by a finite ring if, and only if, it contains only finitely many subvarieties. Also, the Everett extension of a variety by another variety is a locally finite variety (a variety generated by a finite ring) if, and only if, each of the varieties is locally finite (generated by a finite ring).
Proceedings of the American Mathematical Society © 1975 American Mathematical Society