| Title:
|
Characterizations of totally ordered sets by their various endomorphisms (English) |
| Author:
|
Hort, Daniel |
| Author:
|
Chvalina, Jan |
| Author:
|
Moučka, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
23-32 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We characterize totally ordered sets within the class of all ordered sets containing at least three-element chains using a simple relationship between their isotone transformations and the so called 2-, 3-, 4-endomorphisms which are introduced in the paper. Another characterization of totally ordered sets within the class of ordered sets of a locally finite height with at least four-element chains in terms of the regular semigroup theory is also given. (English) |
| Keyword:
|
endomorphisms |
| Keyword:
|
totally ordered sets—chains |
| Keyword:
|
isotone mappings |
| Keyword:
|
regular semigroups |
| MSC:
|
06A05 |
| MSC:
|
20M17 |
| MSC:
|
20M20 |
| idZBL:
|
Zbl 0998.06001 |
| idMR:
|
MR1885454 |
| . |
| Date available:
|
2009-09-24T10:48:44Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127699 |
| . |
| Reference:
|
[1] M. E. Adams and M. Gould: Posets whose monoids of order-preserving maps are regular.Order 6 (1989), 195–201. MR 1031655, 10.1007/BF02034336 |
| Reference:
|
[2] A. Ja. Aizenštat: Regular semigroups of endomorphisms of ordered sets.Uč. zapiski Leningrad. Gos. Ped. Inst. 387 (1968), 3–11. (Russian) MR 0232711 |
| Reference:
|
[3] G. Birkhoff: Lattice Theory.AMS Colloq. Publ. 25, Providence, 1979. Zbl 0505.06001, MR 0598630 |
| Reference:
|
[4] J. Chvalina: Functional Graphs, Quasi-Ordered Sets and Commutative Hypergroups.Vydavatelství Masarykovy Univerzity, Brno, 1995. (Czech) |
| Reference:
|
[5] J. Chvalina and L. Chvalinová: Locally finite rooted trees with regular monoids of local automorphisms.Knižnice odb. věd. spisů VUT v Brně B-119 (1988), 71–86. |
| Reference:
|
[6] P. Corsini: Prolegomena of Hypergroup Theory.Aviani Editore, 1993. Zbl 0785.20032, MR 1237639 |
| Reference:
|
[7] D. Hort: A construction of hypergroups from ordered structures and their morphisms. Presented on the Seventh Sypmposium on AHA, Taormina, Italy 1999.(to appear). MR 2042325 |
| Reference:
|
[8] J. M. Howie: An Introduction to Semigroup Theory.Academic Press, New York, 1976. Zbl 0355.20056, MR 0466355 |
| Reference:
|
[9] J. Jantosciak: Homomorphisms, equivalences and reductions in hypergroups.Riv. di Mat. Pura ed Appl. 9 (1991), 23–47. Zbl 0739.20037, MR 1133589 |
| Reference:
|
[10] L. Kosmák: Set Algebra.Vydavatelství Masarykovy Univerzity, Brno, 1995. (Czech) |
| Reference:
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[11] J. Moučka: Connected functional graphs with regular endomorphism monoids and their hypergroups.Sborník prací PedF MU, Brno 152 (2000), 53–59. (Czech) |
| Reference:
|
[12] J. Novák: On partition of an ordered continuum.Fundamenta Math. XXXIX (1952), 53–64. MR 0056049 |
| . |
