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

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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

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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

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  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) 
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  12. On partition of an ordered continuum, Fundamenta Math. XXXIX (1952), 53–64. (1952) MR0056049

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