A characterization

of minimal locally finite varieties

Authors:
Keith A. Kearnes and Ágnes Szendrei

Journal:
Trans. Amer. Math. Soc. **349** (1997), 1749-1768

MSC (1991):
Primary 08B15; Secondary 08B30

DOI:
https://doi.org/10.1090/S0002-9947-97-01883-7

MathSciNet review:
1407494

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Keith A. Kearnes**

Affiliation:
Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701

Email:
kearnes@comp.uark.edu

**Ágnes Szendrei**

Affiliation:
Bolyai Institute, Aradi vértanúk tere 1, H–6720 Szeged, Hungary

Email:
a.szendrei@sol.cc.u-szeged.hu

DOI:
https://doi.org/10.1090/S0002-9947-97-01883-7

Received by editor(s):
August 7, 1994

Additional Notes:
Research of the first author supported by a fellowship from the Alexander von Humboldt Stiftung

Research of the second author supported by a fellowship from the Alexander von Humboldt Stiftung and by the Hungarian National Foundation for Scientific Research grant no. 1903.

Article copyright:
© Copyright 1997
American Mathematical Society