Lattice of subalgebras in the finitely generated varieties of MV-algebras

Teheux, Bruno

doi:10.1016/j.disc.2006.08.006

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Lattice of subalgebras in the finitely generated varieties of MV-algebras

Teheux, Bruno

2007 • In Discrete Mathematics, 307 (17-18), p. 2261-2275

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https://hdl.handle.net/2268/536

DOI
10.1016/j.disc.2006.08.006

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Keywords :

subalgebra lattices; MV-algebras; natural duality

Abstract :

[en] In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras, With this tool, we obtain the dual atomicity of these lattices, and characterize the members of these varieties in which every subalgebra is an intersection of maximal subalgebras. Then, we determine the algebras that have a modular or distributive lattice of subalgebras.

Disciplines :

Mathematics

Author, co-author :

Teheux, Bruno ; Université de Liège - ULiège > Département de mathématique > Algèbre et logique

Language :

English

Title :

Lattice of subalgebras in the finitely generated varieties of MV-algebras

Publication date :

06 August 2007

Journal title :

Discrete Mathematics

ISSN :

0012-365X

eISSN :

1872-681X

Publisher :

Elsevier Science Bv, Amsterdam, Netherlands

Volume :

307

Issue :

17-18

Pages :

2261-2275

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 08 September 2008

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Bibliography

R. Bonnet, Subalgebras, in: Handbook of Boolean Algebras, vol. 2, North-Holland, Amsterdam, 1989.
Carrega J.C., and Ponasse D. Algèbre et topologie booléennes (1979), Masson, Paris
Chang C.C. Algebraic analysis of many-valued logic. Trans. Amer. Math. Soc. 88 (1958) 467-490
Chang C.C. A new proof of the completeness of the Łukasiewicz axioms. Trans. Amer. Math. Soc. 93 (1959) 74-80
Cignoli R. Natural dualities for the algebras of Łukasiewicz finite-valued logics. Bull. Symbolic Logic 2 (1996) 218
R. Cignoli, I.M.L. D'ottaviano, D. Mundici, Algebraic foundations of many-valued reasoning, Trends in Logic-Studia Logica Library, vol. 7, Kluwer Academic Publishers, Dordrechet, 2000.
Clark D.M., and Davey B.A. Natural Dualities for the Working Algebraist (1998), Cambridge University Press, Cambridge
Di Nola A., and Grigolia R. Projective MV-algebras and their automorphism groups. J. Mult.-Valued Logic Soft Comput. 9 (2003) 291-317
Grigolia R. Free algebras of non-classical logics (1987), Monograph "Metsniereba", Tbilisi (Russian)
R. Grigolia, Algebraic analysis of Łukasiewicz-Tarski n-valued logical systems, Selected Papers on Łukasiewicz Sentential Calculi, Wroclaw, 1997, pp. 81-91.
Hansoul G. Priestley duality for some subalgebra lattices. Studia Logica 56 (1996) 133-149
Komori Y. Super Łukasiewicz propositional logics. Nagoya Math. J. 84 (1981) 119-133
Niederkorn P. Natural dualities for varieties of MV-algebras, I. J. Math. Anal. Appl. 255 (2001) 58-73