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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
MathSciNet review: 1407494
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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: http://dx.doi.org/10.1090/S0002-9947-97-01883-7
PII: S 0002-9947(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