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Locally finite affine complete varieties

Part of: Varieties Algebraic structures

Published online by Cambridge University Press:  09 April 2009

Kalle Kaarli
Kalle Kaarli
Affiliation:
Department of Mathematics University of TartuEE2400 TartuEstonia e-mail: [email protected]
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Abstract

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The main results of the paper are the following: 1. Every locally finite affine complete variety admits a near unanimity term; 2. A locally finite congruence distributive variety is affine complete if and only if all its algebras with no proper subalgebras are affine complete and the variety is generated by one of such algebras. The first of these results sharpens a result of McKenzie asserting that all locally finite affine complete varieties are congruence distributive. The second one generalizes the result by Kaarli and Pixley that characterizes arithmetical affine complete varieties.

Keywords

Affine complete varietiescongruence distributivitynear unanimity functionscompatible function systems

MSC classification

Secondary: 08B10: Congruence modularity, congruence distributivity 08A40: Operations, polynomials, primal algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 2 , April 1997 , pp. 141 - 159
Copyright
Copyright © Australian Mathematical Society 1997

References

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