Congruences in ordered sets and LU compatible equivalences

Václav Snášel; Marek Jukl

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2009)

  • Volume: 48, Issue: 1, page 153-156
  • ISSN: 0231-9721

Abstract

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A concept of equivalence 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

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Snášel, Václav, and Jukl, Marek. "Congruences in ordered sets and LU compatible equivalences." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 48.1 (2009): 153-156. <http://eudml.org/doc/35182>.

@article{Snášel2009,
abstract = {A concept of equivalence 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 = {Snášel, Václav, Jukl, Marek},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Ordered set; morphism; $LU$ compatible equivalence; ordered set; morphism; LU compatible equivalence},
language = {eng},
number = {1},
pages = {153-156},
publisher = {Palacký University Olomouc},
title = {Congruences in ordered sets and LU compatible equivalences},
url = {http://eudml.org/doc/35182},
volume = {48},
year = {2009},
}

TY - JOUR
AU - Snášel, Václav
AU - Jukl, Marek
TI - Congruences in ordered sets and LU compatible equivalences
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2009
PB - Palacký University Olomouc
VL - 48
IS - 1
SP - 153
EP - 156
AB - A concept of equivalence 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 - Ordered set; morphism; $LU$ compatible equivalence; ordered set; morphism; LU compatible equivalence
UR - http://eudml.org/doc/35182
ER -

References

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  1. Chajda, I., Snášel, V., Congruences in ordered sets, Math. Bohem. 123, 1 (1998), 95–100. (1998) MR1618652
  2. Kolibiar, M., Congruence relations and direct decomposition of ordered sets, Acta Sci. Math. (Szeged) 51 (1987), 129–135. (1987) MR0911564
  3. Kolibiar, M., Congruence relations and direct decomposition of ordered sets II, Contributions to General Algebra 6 (1988), 167–171. (1988) MR1078035
  4. Haviar, A., Lihová, J., Varieties of posets, Order 22, 4 (2005), 343–356. (2005) Zbl1109.06002MR2220344
  5. Halaš, R., Congruences on posets, Contributions to General Algebra 12 (2000), 195–210. (2000) MR1777659
  6. Halaš, R., Hort, D., A characterization of 1,2,3,4-endomorphisms of posets, Czech. Math. J. 53, 128 (2003), 213–221. (2003) MR1962010

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