# Convex isomorphism of $Q$-lattices

Mathematica Bohemica (1993)

- Volume: 118, Issue: 1, page 37-42
- ISSN: 0862-7959

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topEmanovský, Petr. "Convex isomorphism of $Q$-lattices." Mathematica Bohemica 118.1 (1993): 37-42. <http://eudml.org/doc/29173>.

@article{Emanovský1993,

abstract = {V. I. Marmazejev introduced in [3] 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 the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the $q$-lattices defined in [2] and to characterize the convex isomorphic $q$-lattices.},

author = {Emanovský, Petr},

journal = {Mathematica Bohemica},

keywords = {quasiorder; convex isomorphism; $q$-lattices; quasiorder; convex isomorphism; -lattices},

language = {eng},

number = {1},

pages = {37-42},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Convex isomorphism of $Q$-lattices},

url = {http://eudml.org/doc/29173},

volume = {118},

year = {1993},

}

TY - JOUR

AU - Emanovský, Petr

TI - Convex isomorphism of $Q$-lattices

JO - Mathematica Bohemica

PY - 1993

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 118

IS - 1

SP - 37

EP - 42

AB - V. I. Marmazejev introduced in [3] 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 the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the $q$-lattices defined in [2] and to characterize the convex isomorphic $q$-lattices.

LA - eng

KW - quasiorder; convex isomorphism; $q$-lattices; quasiorder; convex isomorphism; -lattices

UR - http://eudml.org/doc/29173

ER -

## References

top- Emanovský P., Convex isomorphic ordered sets, Mathematica Bohemica 118 (1993), 29-35. (1993) MR1213830
- Chajda I., Lattices in quasiordered set, Acta Univ. Palack. Olomouc 31 (1992), to appear. (1992) MR1212600
- Marmazejev V. I., The lattice of convex sublattices of a lattice, Mežvuzovskij naučnyj sbornik, Saratov (1986), 50-58. (In Russian.) (1986) MR0957970
- Szász G., Théorie des trellis, Akadémiai Kiadó, Budapest, 1971, (1971)

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