Characterization of posets of intervals

Judita Lihová

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 3, page 171-181
  • ISSN: 0044-8753

Abstract

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If A is a class of partially ordered sets, let P ( A ) denote the system of all posets which are isomorphic to the system of all intervals of A for some A ∈ A . We give an algebraic characterization of elements of P ( A ) for A being the class of all bounded posets and the class of all posets A satisfying the condition that for each a ∈ A there exist a minimal element u and a maximal element v with u ≤ a ≤ v , respectively.

How to cite

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Lihová, Judita. "Characterization of posets of intervals." Archivum Mathematicum 036.3 (2000): 171-181. <http://eudml.org/doc/248538>.

@article{Lihová2000,
abstract = {If $A$ is a class of partially ordered sets, let $P(A)$ denote the system of all posets which are isomorphic to the system of all intervals of $A$ for some $A\in A.$ We give an algebraic characterization of elements of $P(A)$ for $A$ being the class of all bounded posets and the class of all posets $A$ satisfying the condition that for each $a\in A$ there exist a minimal element $u$ and a maximal element $v$ with $u\le a\le v,$ respectively.},
author = {Lihová, Judita},
journal = {Archivum Mathematicum},
keywords = {partially ordered set; interval; partially ordered set; interval of a partially ordered set; interval poset},
language = {eng},
number = {3},
pages = {171-181},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Characterization of posets of intervals},
url = {http://eudml.org/doc/248538},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Lihová, Judita
TI - Characterization of posets of intervals
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 3
SP - 171
EP - 181
AB - If $A$ is a class of partially ordered sets, let $P(A)$ denote the system of all posets which are isomorphic to the system of all intervals of $A$ for some $A\in A.$ We give an algebraic characterization of elements of $P(A)$ for $A$ being the class of all bounded posets and the class of all posets $A$ satisfying the condition that for each $a\in A$ there exist a minimal element $u$ and a maximal element $v$ with $u\le a\le v,$ respectively.
LA - eng
KW - partially ordered set; interval; partially ordered set; interval of a partially ordered set; interval poset
UR - http://eudml.org/doc/248538
ER -

References

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