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Title: Convex isomorphic ordered sets (English)
Author: Emanovský, Petr
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 118
Issue: 1
Year: 1993
Pages: 29-35
Summary lang: English
Category: math
Summary: 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]. (English)
Keyword: convex ordered sets
Keyword: convex isomorphism
MSC: 06A06
MSC: 06A10
MSC: 06B15
idZBL: Zbl 0780.06001
idMR: MR1213830
DOI: 10.21136/MB.1993.126018
Date available: 2009-09-24T20:56:49Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Chajda I.: Complemented ordered sets.Arch. Math. (Brno), to appear. Zbl 0983.06002, MR 1201863
Reference: [2] Chajda I., Rachůnek J.: Forbided configuration for distributive and modular ordered sets.Order 5 (1989), 407-423. MR 1010389, 10.1007/BF00353659
Reference: [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.
Reference: [4] Larmerová J., Rachůnek J.: Translations of Distributive and modular ordered sets.Acta UPO, Fac. rer. nat., 91 (Mathematica XXVII, 1988), 13-23. Zbl 0693.06003, MR 1039879
Reference: [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.) MR 0957970
Reference: [6] Szász G.: Théorie des trellis.Akadémiai Kaidó, Budapest, 1971.


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