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Natural duality via a finite set of relations

Published online by Cambridge University Press:  17 April 2009

László Zádori
László Zádori
Affiliation:
JATE, Bolyai Intézet, Aradi Vértanúk Tere 1, H-6720 Szeged, Hungary
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Abstract

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We present a duality theorem. We give a necessary and sufficient condition for any set of algebraic relations to entail the set of all algebraic relations in Davey and Werner's sense. The main result of the paper states that for a finite algebra a finite set of algebraic relations yields a duality if and only if the set of all algebraic relations can be obtained from it by using four types of relational constructs. Finally, we prove that a finite algebra admits a natural duality if and only if the algebra has a near unanimity term operation, provided that the algebra possesses certain 2k-ary term operations for some k. This is a generalisation of a theorem of Davey, Heindorf and McKenzie.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 51 , Issue 3 , June 1995 , pp. 469 - 478
Copyright
Copyright © Australian Mathematical Society 1995

References

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