A characterization of minimal locally finite varieties |
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| Authors: | Keith A. Kearnes Á gnes Szendrei |
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| Affiliation: | Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701 ; Bolyai Institute, Aradi vértanúk tere 1, H--6720 Szeged, Hungary |
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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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