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ArticleOriginal scientific text

Title

Some properties of congurence relations on orthomodular lattices

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
orthomodular lattice, congruence relation, congruence-regular, congruence-uniform, congruence-permutable

Bibliography

  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.
Discussiones Mathematicae - General Algebra and Applications
2001/21/1
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Pages:
57-66
Main language of publication
English
Received
1999-08-30
Accepted
2001-04-19
Published
2001

DOI: 10.7151/dmgaa.1027

Exact and natural sciences