We introduce a bounded lattice L = (L;∧,∨,0,1), where for each p ∈ L there exists an antitone involution on the interval [p,1]. We show that there exists a binary operation · on L such that L is term equivalent to an algebra A(L) = (L;·,0) (the assigned algebra to L) and we characterize A(L) by simple axioms similar to that of Abbott's implication algebra. We define new operations ⊕ and ¬ on A(L) which satisfy some of the axioms of MV-algebra. Finally we show what properties must be satisfied by L or A(L) to obtain all axioms of MV-algebra.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1073,
author = {Ivan Chajda and Peter Emanovsk\'y},
title = {Bounded lattices with antitone involutions and properties of MV-algebras},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {24},
year = {2004},
pages = {31-42},
zbl = {1082.03055},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1073}
}
Ivan Chajda; Peter Emanovský. Bounded lattices with antitone involutions and properties of MV-algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 31-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1073/
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