| Title:
|
Convex isomorphism of $Q$-lattices (English) |
| Author:
|
Emanovský, Petr |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
118 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
37-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
quasiorder |
| Keyword:
|
convex isomorphism |
| Keyword:
|
$q$-lattices |
| MSC:
|
06A06 |
| MSC:
|
06A10 |
| MSC:
|
06B15 |
| idZBL:
|
Zbl 0780.06002 |
| idMR:
|
MR1213831 |
| DOI:
|
10.21136/MB.1993.126019 |
| . |
| Date available:
|
2009-09-24T20:56:57Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126019 |
| . |
| Reference:
|
[1] Emanovský P.: Convex isomorphic ordered sets.Mathematica Bohemica 118 (1993), 29-35. MR 1213830 |
| Reference:
|
[2] Chajda I.: Lattices in quasiordered set.Acta Univ. Palack. Olomouc 31 (1992), to appear. MR 1212600 |
| Reference:
|
[3] Marmazejev V. I.: The lattice of convex sublattices of a lattice.Mežvuzovskij naučnyj sbornik, Saratov (1986), 50-58. (In Russian.) MR 0957970 |
| Reference:
|
[4] Szász G.: Théorie des trellis.Akadémiai Kiadó, Budapest, 1971, |
| . |
