# 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

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topHort, 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 -

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