| Title:
|
A characterization of 1-, 2-, 3-, 4-homomorphisms of ordered sets (English) |
| Author:
|
Halaš, Radomír |
| Author:
|
Hort, Daniel |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
213-221 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
ordered sets |
| Keyword:
|
morphisms |
| MSC:
|
06A05 |
| MSC:
|
06A06 |
| MSC:
|
06A10 |
| MSC:
|
06A99 |
| idZBL:
|
Zbl 1015.06002 |
| idMR:
|
MR1962010 |
| . |
| Date available:
|
2009-09-24T11:00:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127792 |
| . |
| Reference:
|
[1] G. Grätzer: General Lattice Theory.Akademie-Verlag, Berlin, 1978, Russian translation 1982. MR 0504338 |
| Reference:
|
[2] R. Halaš: Congruences on posets.Contributions to General Algebra No. 12, Verlag J. Heyn, Klagenfurt, 2000, pp. 195–210. MR 1777659 |
| Reference:
|
[3] D. Hort: A construction of hypergroups from ordered structures and their morphisms.Preprint (1998). MR 2042325 |
| Reference:
|
[4] D. Hort, J. Chvalina and J. Moučka: Characterizations of totally ordered sets by their various endomorphisms.Czechoslovak Math. J. 52 (2002), 23–32. MR 1885454, 10.1023/A:1021763102781 |
| Reference:
|
[5] J. Jantosciak: Homomorphisms, equivalences and reductions in hypergroups.Riv. Mat. Pura Appl. 9 (1991), 23–47. Zbl 0739.20037, MR 1133589 |
| . |
