A characterization of minimal locally finite varieties
Authors:
Keith A. Kearnes and Ágnes Szendrei
Journal:
Trans. Amer. Math. Soc. 349 (1997), 17491768
MSC (1991):
Primary 08B15; Secondary 08B30
MathSciNet review:
1407494
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Abstract: In this paper we describe a onevariable Mal'cevlike 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'cevlike 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.uszeged.hu
DOI:
http://dx.doi.org/10.1090/S0002994797018837
PII:
S 00029947(97)018837
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
