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ArticleOriginal scientific text

Title

Distributivity of bounded lattices with sectionally antitone involutions

Authors 1

Affiliations

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

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

ENG
sectionally antitone involution, bounded lattice, distributive lattice, MV-algebra

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2005/25/2
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Pages:
155-163
Main language of publication
English
Received
2004-10-06
Published
2005

DOI: 10.7151/dmgaa.1098

Exact and natural sciences