Locally finite ring varieties

Iskander, Awad A.

doi:10.1090/S0002-9939-1975-0369428-8

Locally finite ring varieties
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by Awad A. Iskander PDF

Proc. Amer. Math. Soc. 50 (1975), 28-32 Request permission

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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