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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