Congruences in ordered sets

Ivan Chajda; Václav Snášel

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 1, page 95-100
  • ISSN: 0862-7959

Abstract

top
A concept of congruence preserving upper and lower bounds in a poset P is introduced. If P is a lattice, this concept coincides with the notion of lattice congruence.

How to cite

top

Chajda, Ivan, and Snášel, Václav. "Congruences in ordered sets." Mathematica Bohemica 123.1 (1998): 95-100. <http://eudml.org/doc/248300>.

@article{Chajda1998,
abstract = {A concept of congruence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence.},
author = {Chajda, Ivan, Snášel, Václav},
journal = {Mathematica Bohemica},
keywords = {congruence preserving upper and lower bounds; morphism; lattice congruence; poset; ordered set; lower and upper bounds; congruence preserving upper and lower bounds; morphism; lattice congruence; poset},
language = {eng},
number = {1},
pages = {95-100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Congruences in ordered sets},
url = {http://eudml.org/doc/248300},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Chajda, Ivan
AU - Snášel, Václav
TI - Congruences in ordered sets
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 1
SP - 95
EP - 100
AB - A concept of congruence preserving upper and lower bounds in a poset $P$ is introduced. If $P$ is a lattice, this concept coincides with the notion of lattice congruence.
LA - eng
KW - congruence preserving upper and lower bounds; morphism; lattice congruence; poset; ordered set; lower and upper bounds; congruence preserving upper and lower bounds; morphism; lattice congruence; poset
UR - http://eudml.org/doc/248300
ER -

References

top
  1. G. Dorfer, Sublattice-extensions by means of convex sublattices, Contributions to General Algebra 9. Verlag Hölder-Pichler-Temski, Wien, 1995, pp. 127-132. (1995) MR1484432
  2. G. Grätzer, General Lattice Theory, Birkhäuser, Basel-Stuttgart, 1987. (1987) 
  3. M. Kolibiar, Congruence relations and direct decomposition of ordered sets, Acta Sci. Math. (Szeged) 51 (1987), 129-135. (1987) MR0911564

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.