Monotone clones, residual smallness and congruence distributivity. (English) Zbl 0695.08012
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. The author gives several characterisations of the finite bounded ordered sets for which the corresponding variety is congruence-distributive.
Reviewer: A.Hatvany
MSC:
08B10 | Congruence modularity, congruence distributivity |
06A06 | Partial orders, general |
08A40 | Operations and polynomials in algebraic structures, primal algebras |
Keywords:
clones; residual smallness; congruence distributivity; monotone operations; finite bounded ordered setsReferences:
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