Characterizations of totally ordered sets by their various endomorphisms

Daniel Hort; Jan Chvalina; Jiří Moučka

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 1, page 23-32
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Hort, Daniel, Chvalina, Jan, and Moučka, Jiří. "Characterizations of totally ordered sets by their various endomorphisms." Czechoslovak Mathematical Journal 52.1 (2002): 23-32. <http://eudml.org/doc/30682>.

@article{Hort2002,
abstract = {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.},
author = {Hort, Daniel, Chvalina, Jan, Moučka, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {endomorphisms; totally ordered sets—chains; isotone mappings; regular semigroups; endomorphisms; totally ordered sets; isotone mappings; regular semigroups; chains},
language = {eng},
number = {1},
pages = {23-32},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of totally ordered sets by their various endomorphisms},
url = {http://eudml.org/doc/30682},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Hort, Daniel
AU - Chvalina, Jan
AU - Moučka, Jiří
TI - Characterizations of totally ordered sets by their various endomorphisms
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 23
EP - 32
AB - 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.
LA - eng
KW - endomorphisms; totally ordered sets—chains; isotone mappings; regular semigroups; endomorphisms; totally ordered sets; isotone mappings; regular semigroups; chains
UR - http://eudml.org/doc/30682
ER -

References

top
  1. 10.1007/BF02034336, Order 6 (1989), 195–201. (1989) MR1031655DOI10.1007/BF02034336
  2. Regular semigroups of endomorphisms of ordered sets, Uč. zapiski Leningrad. Gos. Ped. Inst. 387 (1968), 3–11. (Russian) (1968) MR0232711
  3. Lattice Theory, AMS Colloq. Publ. 25, Providence, 1979. (1979) Zbl0505.06001MR0598630
  4. Functional Graphs, Quasi-Ordered Sets and Commutative Hypergroups, Vydavatelství Masarykovy Univerzity, Brno, 1995. (Czech) (1995) 
  5. Locally finite rooted trees with regular monoids of local automorphisms, Knižnice odb. věd. spisů VUT v Brně B-119 (1988), 71–86. (1988) 
  6. Prolegomena of Hypergroup Theory, Aviani Editore, 1993. (1993) Zbl0785.20032MR1237639
  7. A construction of hypergroups from ordered structures and their morphisms. Presented on the Seventh Sypmposium on AHA, Taormina, Italy 1999, (to appear). (to appear) MR2042325
  8. An Introduction to Semigroup Theory, Academic Press, New York, 1976. (1976) Zbl0355.20056MR0466355
  9. Homomorphisms, equivalences and reductions in hypergroups, Riv. di Mat. Pura ed Appl. 9 (1991), 23–47. (1991) Zbl0739.20037MR1133589
  10. Set Algebra, Vydavatelství Masarykovy Univerzity, Brno, 1995. (Czech) (1995) 
  11. Connected functional graphs with regular endomorphism monoids and their hypergroups, Sborník prací PedF MU, Brno 152 (2000), 53–59. (Czech) (2000) 
  12. On partition of an ordered continuum, Fundamenta Math. XXXIX (1952), 53–64. (1952) MR0056049

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.