In this paper congruences on orthomodular lattices are studied with particular regard to analogies in Boolean algebras. For this reason the lattice of p-ideals (corresponding to the congruence lattice) and the interplay between congruence classes is investigated. From the results adduced there, congruence regularity, uniformity and permutability for orthomodular lattices can be derived easily.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1027,
author = {Gerhard Dorfer},
title = {Some properties of congurence relations on orthomodular lattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {21},
year = {2001},
pages = {57-66},
zbl = {1011.06011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1027}
}
Gerhard Dorfer. Some properties of congurence relations on orthomodular lattices. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 57-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1027/
[000] [1] L. Beran, Orthomodular Lattices, D. Reidel Publishing Company, Dordrecht-Boston 1985.
[001] [2] R.P. Dilworth, The structure of relatively complemented lattices, Ann. of Math. 51 (1950), 348-359. | Zbl 0036.01802
[002] [3] P.D. Finch, Congruence relations on orthomodular lattices, J. Austral. Math. Soc. 6 (1966), 46-54. | Zbl 0141.00904
[003] [4] J. Hashimoto, Congruence relations and congruence classes in lattices, Osaka Math. J. 15 (1963), 71-86. | Zbl 0119.01801
[004] [5] G. Kalmbach, Orthomodular Lattices, Academic Press, London 1983.
[005] [6] T. Katrinák, Die Kennzeichnung der distributiven pseudokomplementären Halbverbände, J. Reine Angew. Math. 241 (1970), 160-179. | Zbl 0192.33503
[006] [7] P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer Academic Publishers, Dordrecht 1991.