Residuation in orthomodular lattices

@article{IvanChajda2017,
abstract = {We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.},
author = {Ivan Chajda, Helmut Länger},
journal = {Topological Algebra and its Applications},
keywords = {residuated lattice; right residuated lattice; weak residuated lattice; orthomodular lattice; weak divisible; positive; double negation law},
language = {eng},
number = {1},
pages = {1-5},
title = {Residuation in orthomodular lattices},
url = {http://eudml.org/doc/288133},
volume = {5},
year = {2017},
}

TY - JOUR
AU - Ivan Chajda
AU - Helmut Länger
TI - Residuation in orthomodular lattices
JO - Topological Algebra and its Applications
PY - 2017
VL - 5
IS - 1
SP - 1
EP - 5
AB - We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness. Moreover, we show that every positive right residuated lattice satisfying the double negation law and two further simple identities can be converted into an orthomodular lattice. In this case, also the converse statement is true and the corresponence is nearly one-to-one.
LA - eng
KW - residuated lattice; right residuated lattice; weak residuated lattice; orthomodular lattice; weak divisible; positive; double negation law
UR - http://eudml.org/doc/288133
ER -