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Monotone clones, residual smallness and congruence distributivity

Published online by Cambridge University Press:  17 April 2009

Ralph McKenzie
Ralph McKenzie
Affiliation:
Department of MathematicsUniversity of CaliforniaBerkeley, California 94720United States of America
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Abstract

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Corresponding to each ordered set there is a variety, determined up to equivalence, generated by an algebra whose term operations are all the monotone operations on the ordered set. We produce several characterisations of the finite bounded ordered sets for which the corresponding variety is congruence-distributive. In particular, we find that congruence-distributivity, congruence-modularity, and residual smallness are equivalent for these varieties.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 41 , Issue 2 , April 1990 , pp. 283 - 300
Copyright
Copyright © Australian Mathematical Society 1990

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