Convex isomorphic ordered sets

Petr Emanovský

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 1, page 29-35
  • ISSN: 0862-7959

Abstract

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V. I. Marmazejev introduced in [5] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered sets. These concepts were defined in [1], [2], [4].

How to cite

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Emanovský, Petr. "Convex isomorphic ordered sets." Mathematica Bohemica 118.1 (1993): 29-35. <http://eudml.org/doc/29172>.

@article{Emanovský1993,
abstract = {V. I. Marmazejev introduced in [5] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered sets. These concepts were defined in [1], [2], [4].},
author = {Emanovský, Petr},
journal = {Mathematica Bohemica},
keywords = {convex ordered sets; convex isomorphism; convex ordered sets; convex isomorphism},
language = {eng},
number = {1},
pages = {29-35},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convex isomorphic ordered sets},
url = {http://eudml.org/doc/29172},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Emanovský, Petr
TI - Convex isomorphic ordered sets
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 1
SP - 29
EP - 35
AB - V. I. Marmazejev introduced in [5] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered sets. These concepts were defined in [1], [2], [4].
LA - eng
KW - convex ordered sets; convex isomorphism; convex ordered sets; convex isomorphism
UR - http://eudml.org/doc/29172
ER -

References

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  1. Chajda I., Complemented ordered sets, Arch. Math. (Brno), to appear. Zbl0983.06002MR1201863
  2. Chajda I., Rachůnek J., 10.1007/BF00353659, Order 5 (1989), 407-423. (1989) MR1010389DOI10.1007/BF00353659
  3. Igosin V. I., Lattices of intervals and lattices of convex sublattices of lattices, (Russian), Mežvuzovskij naučnyj sbornik 6-Uporjadočennyje množestva i rešetky, Saratov (1980), 69-76. (1980) 
  4. Larmerová J., Rachůnek J., Translations of Distributive and modular ordered sets, Acta UPO, Fac. rer. nat., 91 (Mathematica XXVII, 1988), 13-23. (1988) Zbl0693.06003MR1039879
  5. Marmazejev V. I., The lattice of convex sublattices of a lattice, Mežvuzovskij naučnyj sbornik 6-Uporjadočennyje množestva i rešetky, Saratov (1986), 50-58. (In Russian.) (1986) MR0957970
  6. Szász G., Théorie des trellis, Akadémiai Kaidó, Budapest, 1971. (1971) 

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