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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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 $ {{\mathbf{B}}_n}(3 \leq n < \omega )$ of pseudocomplemented distributive lattices there exists a natural duality given by a set of $ p(n) + 3$ binary algebraic relations, where $ p(n)$ denotes the number of partitions of $ n$. This paper improves this result by establishing that an optimal set of $ n + 3$ 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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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1169079-7
PII: S 0002-9947(1993)1169079-7
Keywords: Distributive $ p$-algebra, natural duality, piggyback duality, optimal duality
Article copyright: © Copyright 1993 American Mathematical Society