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.
@article{bwmeta1.element.doi-10_1515_taa-2017-0001,
author = {Ivan Chajda and Helmut L\"anger},
title = {Residuation in orthomodular lattices},
journal = {Topological Algebra and its Applications},
volume = {5},
year = {2017},
pages = {1-5},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_taa-2017-0001}
}
Ivan Chajda; Helmut Länger. Residuation in orthomodular lattices. Topological Algebra and its Applications, Tome 5 (2017) pp. 1-5. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_taa-2017-0001/