A Characterization of Minimal Locally Finite Varieties

Kearnes, Keith; Szendrei, Ágnes

doi:10.1090/S0002-9947-97-01883-7

A Characterization of Minimal Locally Finite Varieties
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by Keith A. Kearnes and Ágnes Szendrei PDF

Trans. Amer. Math. Soc. 349 (1997), 1749-1768 Request permission

Abstract:

In this paper we describe a one–variable Mal′cev–like condition satisfied by any locally finite minimal variety. We prove that a locally finite variety is minimal if and only if it satisfies this Mal′cev–like condition and it is generated by a strictly simple algebra which is nonabelian or has a trivial subalgebra. Our arguments show that the strictly simple generator of a minimal locally finite variety is unique, it is projective and it embeds into every member of the variety. We give a new proof of the structure theorem for strictly simple abelian algebras that generate minimal varieties.

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