Some properties of congurence relations on orthomodular lattices

• Autorzy: Gerhard Dorfer
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

orthomodular lattice; congruence relation; congruence-regular; congruence-uniform; congruence-permutable

Kategorie tematyczne

• 06C15: Complemented lattices, orthocomplemented lattices and posets
• 03G12: Quantum logic
• 08A30: Subalgebras, congruence relations
• 81P10: Logical foundations of quantum mechanics; quantum logic

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2001
• Tom: 21
• Numer: 1
• Strony: 57-66

Daty

wydano

2001

otrzymano

1999-08-30

poprawiono

2001-04-19

Twórcy

autor

Gerhard Dorfer

• Institute of Algebra and Computational Mathematics, Vienna University of Technology, Wiedner Hauptstr. 8-10/118, A-1040 Vienna, Austria

Bibliografia

• [1] L. Beran, Orthomodular Lattices, D. Reidel Publishing Company, Dordrecht-Boston 1985.
• [2] R.P. Dilworth, The structure of relatively complemented lattices, Ann. of Math. 51 (1950), 348-359.
• [3] P.D. Finch, Congruence relations on orthomodular lattices, J. Austral. Math. Soc. 6 (1966), 46-54.
• [4] J. Hashimoto, Congruence relations and congruence classes in lattices, Osaka Math. J. 15 (1963), 71-86.
• [5] G. Kalmbach, Orthomodular Lattices, Academic Press, London 1983.
• [6] T. Katrinák, Die Kennzeichnung der distributiven pseudokomplementären Halbverbände, J. Reine Angew. Math. 241 (1970), 160-179.
• [7] P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer Academic Publishers, Dordrecht 1991.

Identyfikatory

DOI

10.7151/dmgaa.1027