Some properties of congurence relations on orthomodular lattices

Gerhard Dorfer

Discussiones Mathematicae - General Algebra and Applications (2001)

  • Volume: 21, Issue: 1, page 57-66
  • ISSN: 1509-9415

Abstract

top
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.

How to cite

top

Gerhard Dorfer. "Some properties of congurence relations on orthomodular lattices." Discussiones Mathematicae - General Algebra and Applications 21.1 (2001): 57-66. <http://eudml.org/doc/287619>.

@article{GerhardDorfer2001,
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.},
author = {Gerhard Dorfer},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {orthomodular lattice; congruence relation; congruence-regular; congruence-uniform; congruence-permutable; -ideal; congruence class; congruence regular; congruence uniform; arithmetical},
language = {eng},
number = {1},
pages = {57-66},
title = {Some properties of congurence relations on orthomodular lattices},
url = {http://eudml.org/doc/287619},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Gerhard Dorfer
TI - Some properties of congurence relations on orthomodular lattices
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2001
VL - 21
IS - 1
SP - 57
EP - 66
AB - 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.
LA - eng
KW - orthomodular lattice; congruence relation; congruence-regular; congruence-uniform; congruence-permutable; -ideal; congruence class; congruence regular; congruence uniform; arithmetical
UR - http://eudml.org/doc/287619
ER -

References

top
  1. [1] L. Beran, Orthomodular Lattices, D. Reidel Publishing Company, Dordrecht-Boston 1985. 
  2. [2] R.P. Dilworth, The structure of relatively complemented lattices, Ann. of Math. 51 (1950), 348-359. Zbl0036.01802
  3. [3] P.D. Finch, Congruence relations on orthomodular lattices, J. Austral. Math. Soc. 6 (1966), 46-54. Zbl0141.00904
  4. [4] J. Hashimoto, Congruence relations and congruence classes in lattices, Osaka Math. J. 15 (1963), 71-86. Zbl0119.01801
  5. [5] G. Kalmbach, Orthomodular Lattices, Academic Press, London 1983. 
  6. [6] T. Katrinák, Die Kennzeichnung der distributiven pseudokomplementären Halbverbände, J. Reine Angew. Math. 241 (1970), 160-179. Zbl0192.33503
  7. [7] P. Pták and S. Pulmannová, Orthomodular Structures as Quantum Logics, Kluwer Academic Publishers, Dordrecht 1991. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.