DM-GAA

ISSN 1509-9415 (print version)

ISSN 2084-0373 (electronic version)

https://doi.org/10.7151/dmgaa

Discussiones Mathematicae - General Algebra and Applications

Cite Score: 0.4

SJR: 0.203

SNIP: 0.562

MCQ: 0.12

Index Copernicus: 121.02

Discussiones Mathematicae - General Algebra and Applications

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Discussiones Mathematicae General Algebra and Applications 25(2) (2005) 155-163
DOI: https://doi.org/10.7151/dmgaa.1098

DISTRIBUTIVITY OF BOUNDED LATTICES WITH SECTIONALLY ANTITONE INVOLUTIONS

Ivan Chajda

Department of Algebra and Geometry
Palacký University of Olomouc
Tomkova 40, 779 00 Olomouc, Czech Republic

e-mail: chajda@inf.upol.cz

Abstract

We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L   is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.

Keywords: sectionally antitone involution, bounded lattice, distributive lattice, MV-algebra.

2000 Mathematics Subject Classification: 06A12, 06D35, 06F35.

References

[1] J.C. Abbott, Semi-boolean algebra, Matem. Vestnik 4 (1967), 177-198.
[2] R.L.O. Cignoli, I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer, Dordrecht/Boston/London 2000.
[3] I. Chajda, Lattices and semilattices having an antitone involution inevery upper interval, Comment. Math. Univ. Carol (CMUC) 44 (4) (2003), 577-585.
[4] I. Chajda and P. Emanovský, Bounded lattices with antitone involutions and properties of MV-algebras, Discuss. Math. General Algebra and Appl. 24 (2004), 31-42.
[5] I. Chajda, R. Halas and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged), to appear.

Received 6 October 2004


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