Geodesic
A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 213-221 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 06A05, 06A06, 06A10, 06A99
Keywords: ordered sets; morphisms 
@article{CMJ_2003_53_1_a16,
     author = {Hala\v{s}, Radom{\'\i}r and Hort, Daniel},
     title = {A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {213--221},
     year = {2003},
     volume = {53},
     number = {1},
     mrnumber = {1962010},
     zbl = {1015.06002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a16/}
}
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
SP  - 213
EP  - 221
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a16/
LA  - en
ID  - CMJ_2003_53_1_a16
ER  - 
%0 Journal Article
%A Halaš, Radomír
%A Hort, Daniel
%T A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets
%J Czechoslovak Mathematical Journal
%D 2003
%P 213-221
%V 53
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a16/
%G en
%F CMJ_2003_53_1_a16
Halaš, Radomír; Hort, Daniel. A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 1, pp. 213-221. http://geodesic.mathdoc.fr/item/CMJ_2003_53_1_a16/

[1] G. Grätzer: General Lattice Theory. Akademie-Verlag, Berlin, 1978, Russian translation 1982. | MR

[2] R. Halaš: Congruences on posets. Contributions to General Algebra No.  12, Verlag J. Heyn, Klagenfurt, 2000, pp. 195–210. | MR

[3] D.  Hort: A construction of hypergroups from ordered structures and their morphisms. Preprint (1998). | MR

[4] D. Hort, J. Chvalina and J. Moučka: Characterizations of totally ordered sets by their various endomorphisms. Czechoslovak Math. J. 52 (2002), 23–32. | DOI | MR

[5] J. Jantosciak: Homomorphisms, equivalences and reductions in hypergroups. Riv. Mat. Pura Appl. 9 (1991), 23–47. | MR | Zbl