Optimal natural dualities

Authors:
B. A. Davey and H. A. Priestley

Journal:
Trans. Amer. Math. Soc. **338** (1993), 655-677

MSC:
Primary 06D15

MathSciNet review:
1169079

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Abstract: The authors showed previously that for each of the varieties of pseudocomplemented distributive lattices there exists a natural duality given by a set of binary algebraic relations, where denotes the number of partitions of . This paper improves this result by establishing that an optimal set of of these relations suffices. This is achieved by the use of "test algebras": it is shown that redundancy among the relations of a duality for a prevariety generated by a finite algebra may be decided by testing the duality on the relations, *qua* algebras.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1993-1169079-7

Keywords:
Distributive -algebra,
natural duality,
piggyback duality,
optimal duality

Article copyright:
© Copyright 1993
American Mathematical Society