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Transferring Optimal Dualities: Theory and Practice

Part of: Boolean algebras (Boolean rings) Other classes of algebra Algebraic structures Distributive lattices

Published online by Cambridge University Press:  09 April 2009

B. A. Davey  and
M. Haviar
B. A. Davey
Affiliation:
School of Mathematics La Trobe University VIC 3086 Australia e-mail: B.Davey@latrobe.edu.au
M. Haviar
Affiliation:
Department of Mathematics M. Bel UniversityPdF, Ruzova 13 974 01 Banska Bystrica Slovak Republic e-mail: haviar@pdf.umb.sk
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Abstract

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Consider the quasi-variety generated by a finite algebra and assume that yields a natural duality on based on which is optimal modulo endomorphisms. We shoe that, provided satisfies certain minimality conditions, we can transfer this duality to a natural duality on based on , which is also optimal modulo endormorphisms, for any finite algebra in that has a subalgebra isomorphic to .

Keywords

natural dualityoptimal dualityendodualisabilityendoprimalityglobally minimal failsetentailmentretractiondistributive latticeKleene algebraStone algebra.

MSC classification

Secondary: 08C15: Quasivarieties 08A99: None of the above, but in this section 06D50: Lattices and duality 06D15: Pseudocomplemented lattices 06D30: De Morgan algebras, L ukasiewicz algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 3 , June 2003 , pp. 393 - 420
Copyright
Copyright © Australian Mathematical Society 2003

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