A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets

Radomír Halaš; Daniel Hort

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 1, page 213-221
  • ISSN: 0011-4642

Abstract

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We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.

How to cite

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Halaš, Radomír, and Hort, Daniel. "A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets." Czechoslovak Mathematical Journal 53.1 (2003): 213-221. <http://eudml.org/doc/30770>.

@article{Halaš2003,
abstract = {We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.},
author = {Halaš, Radomír, Hort, Daniel},
journal = {Czechoslovak Mathematical Journal},
keywords = {ordered sets; morphisms; totally ordered sets; morphisms; four-element chains},
language = {eng},
number = {1},
pages = {213-221},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets},
url = {http://eudml.org/doc/30770},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Halaš, Radomír
AU - Hort, Daniel
TI - A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 213
EP - 221
AB - We characterize totally ordered sets within the class of all ordered sets containing at least four-element chains. We use a simple relationship between their isotone transformations and the so called 1-endomorphism which is introduced in the paper. Later we describe 1-, 2-, 3-, 4-homomorphisms of ordered sets in the language of super strong mappings.
LA - eng
KW - ordered sets; morphisms; totally ordered sets; morphisms; four-element chains
UR - http://eudml.org/doc/30770
ER -

References

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  1. General Lattice Theory, Akademie-Verlag, Berlin, 1978, Russian translation 1982. (1978) MR0504338
  2. Congruences on posets, Contributions to General Algebra No.  12, Verlag J. Heyn, Klagenfurt, 2000, pp. 195–210. (2000) MR1777659
  3. A construction of hypergroups from ordered structures and their morphisms, Preprint (1998). (1998) MR2042325
  4. 10.1023/A:1021763102781, Czechoslovak Math. J. 52 (2002), 23–32. (2002) MR1885454DOI10.1023/A:1021763102781
  5. Homomorphisms, equivalences and reductions in hypergroups, Riv. Mat. Pura Appl. 9 (1991), 23–47. (1991) Zbl0739.20037MR1133589

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