Optimal natural dualities. II: General theory
Authors:
B. A. Davey and H. A. Priestley
Journal:
Trans. Amer. Math. Soc. 348 (1996), 36733711
MSC (1991):
Primary 08B99, 06D15, 06D05, 18A40
MathSciNet review:
1348858
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Abstract: A general theory of optimal natural dualities is presented, built on the test algebra technique introduced in an earlier paper. Given that a set of finitary algebraic relations yields a duality on a class of algebras , those subsets of which yield optimal dualities are characterised. Further, the manner in which the relations in are constructed from those in is revealed in the important special case that generates a congruencedistributive variety and is such that each of its subalgebras is subdirectly irreducible. These results are obtained by studying a certain algebraic closure operator, called entailment, definable on any set of algebraic relations on . Applied, by way of illustration, to the variety of Kleene algebras and to the proper subvarieties of pseudocomplemented distributive lattices, the theory improves upon and illuminates previous results.
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Additional Information
B. A. Davey
Affiliation:
Department of Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia
Email:
B.Davey@latrobe.edu.au
H. A. Priestley
Affiliation:
Mathematical Institute, 24/29 St. Giles, Oxford OX1 3LB, England
Email:
hap@maths.ox.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002994796016017
PII:
S 00029947(96)016017
Keywords:
Natural duality,
optimal duality
Received by editor(s):
August 7, 1994
Received by editor(s) in revised form:
August 29, 1995
Article copyright:
© Copyright 1996 American Mathematical Society
