# Convex isomorphic ordered sets

Mathematica Bohemica (1993)

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

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topEmanovský, 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

top- Chajda I., Complemented ordered sets, Arch. Math. (Brno), to appear. Zbl0983.06002MR1201863
- Chajda I., Rachůnek J., 10.1007/BF00353659, Order 5 (1989), 407-423. (1989) MR1010389DOI10.1007/BF00353659
- 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)
- 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
- 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
- Szász G., Théorie des trellis, Akadémiai Kaidó, Budapest, 1971. (1971)

## Citations in EuDML Documents

top- Petr Emanovský, Convex isomorphism of $Q$-lattices
- Danica Jakubíková-Studenovská, Convex automorphisms of partial monounary algebras
- Ivan Chajda, Petr Emanovský, $\Sigma $-isomorphic algebraic structures
- Ivan Chajda, Petr Emanovský, Modularity and distributivity of the lattice of $\Sigma $-closed subsets of an algebraic structure
- Judita Lihová, On convexly isomorphic posets

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