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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1098,
author = {Ivan Chajda},
title = {Distributivity of bounded lattices with sectionally antitone involutions},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {25},
year = {2005},
pages = {155-163},
zbl = {1100.06008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1098}
}
Ivan Chajda. Distributivity of bounded lattices with sectionally antitone involutions. Discussiones Mathematicae - General Algebra and Applications, Tome 25 (2005) pp. 155-163. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1098/
[000] [1] J.C. Abbott, Semi-boolean algebra, Matem. Vestnik 4 (1967), 177-198. | Zbl 0153.02704
[001] [2] R.L.O. Cignoli, I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer, Dordrecht/Boston/London 2000. | Zbl 0937.06009
[002] [3] I. Chajda, Lattices and semilattices having an antitone involution inevery upper interval, Comment. Math. Univ. Carol (CMUC) 44 (4) (2003), 577-585. | Zbl 1101.06003
[003] [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. | Zbl 1082.03055
[004] [5] I. Chajda, R. Halas and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged), to appear. | Zbl 1099.06006