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Dualities for some De Morgan algebras with operators and Lukasiewicz algebras

Part of: Distributive lattices Varieties Algebraic logic Boolean algebras (Boolean rings)

Published online by Cambridge University Press:  09 April 2009

Roberto Cignoli  and
Marta S. De Gallego
Roberto Cignoli
Affiliation:
Instituto de MatemáticaUniversidade Estadual de Campinas13.100-Campinas-Sā Paulo-Brazil
Marta S. De Gallego
Affiliation:
Instituto de MatemáticaUniversidade Estadual de Campinas13.100-Campinas-Sā Paulo-Brazil
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Abstract

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Algebras (A, ∧, ∨, ~, γ, 0, 1) of type (2,2,1,1,0,0) such that (A, ∧, ∨, ~, γ 0, 1) is a De Morgan algebra and γ is a lattice homomorphism from A into its center that satisfies one of the conditions (i) a ≤ γa or (ii) a ≤ ~ a ∧ γa are considered. The dual categories and the lattice of their subvarieties are determined, and applications to Lukasiewicz algebras are given.

MSC classification

Secondary: 06D30: De Morgan algebras, L ukasiewicz algebras 03G20: Łukasiewicz and Post algebras 03G25: Other algebras related to logic 08B15: Lattices of varieties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 3 , June 1983 , pp. 377 - 393
Copyright
Copyright © Australian Mathematical Society 1983

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