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Proceedings of the American Mathematical Society

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Locally finite ring varieties


Author: Awad A. Iskander
Journal: Proc. Amer. Math. Soc. 50 (1975), 28-32
MSC: Primary 16A48
DOI: https://doi.org/10.1090/S0002-9939-1975-0369428-8
MathSciNet review: 0369428
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Abstract: 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).


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0369428-8
Keywords: Locally finite varieties of associative rings, equational classes, lattice of varieties, polynomial identities, free members in a variety, variety generated by a finite ring
Article copyright: © Copyright 1975 American Mathematical Society

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