Distributivity of bounded lattices with sectionally antitone involutions
Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 2, pp. 155-163
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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
@article{DMGAA_2005_25_2_a2,
author = {Chajda, Ivan},
title = {Distributivity of bounded lattices with sectionally antitone involutions},
journal = {Discussiones Mathematicae. General Algebra and Applications},
pages = {155--163},
year = {2005},
volume = {25},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGAA_2005_25_2_a2/}
}
TY - JOUR AU - Chajda, Ivan TI - Distributivity of bounded lattices with sectionally antitone involutions JO - Discussiones Mathematicae. General Algebra and Applications PY - 2005 SP - 155 EP - 163 VL - 25 IS - 2 UR - http://geodesic.mathdoc.fr/item/DMGAA_2005_25_2_a2/ LA - en ID - DMGAA_2005_25_2_a2 ER -
Chajda, Ivan. Distributivity of bounded lattices with sectionally antitone involutions. Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 2, pp. 155-163. http://geodesic.mathdoc.fr/item/DMGAA_2005_25_2_a2/
[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.