Bounded lattices with antitone involutions and properties of MV-algebras

Ivan Chajda, and Peter Emanovský. "Bounded lattices with antitone involutions and properties of MV-algebras." Discussiones Mathematicae - General Algebra and Applications 24.1 (2004): 31-42. <http://eudml.org/doc/287754>.

@article{IvanChajda2004,
abstract = {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.},
author = {Ivan Chajda, Peter Emanovský},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {antitone involution; distributive lattice; implication algebra; MV-algebra; bounded lattice},
language = {eng},
number = {1},
pages = {31-42},
title = {Bounded lattices with antitone involutions and properties of MV-algebras},
url = {http://eudml.org/doc/287754},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Ivan Chajda
AU - Peter Emanovský
TI - Bounded lattices with antitone involutions and properties of MV-algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 1
SP - 31
EP - 42
AB - 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.
LA - eng
KW - antitone involution; distributive lattice; implication algebra; MV-algebra; bounded lattice
UR - http://eudml.org/doc/287754
ER -