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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  7. Selfduality of the system of intervals of a partially ordered set, Czechoslov. Math. J. 41 (1991), 135–140. (1991) MR1087633
  8. Systems of intervals of partially ordered sets, Math. Slovaca 46 (1996 No. 4), 355–361. (1996 No. 4) MR1472629
  9. Intervals, convex sublattices and subdirect representations of lattices, Universal Algebra and Applications, Banach Center Publications, Vol. 9, Warsaw 1982, 335–339. Zbl0506.06003MR0738826
  10. Posets having a selfdual interval poset, Czechoslov. Math. J. 44 (1994), 523–533. (1994) MR1288170
  11. On posets with isomorphic interval posets, Czechoslov. Math. J. 49 (1999), 67–80. (1999) MR1676841
  12. On lattices with isomorphic interval lattices, Czechoslov. Math. J. 35 (1985), 550–554. (1985) MR0809041

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