| Title:
|
A remark on $\lambda$-regular orthomodular lattices (English) |
| Author:
|
Rogalewicz, Vladimír |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
6 |
| Year:
|
1989 |
| Pages:
|
449-452 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality $k$ is called $\lambda$-regular, if each atom is a member of just $\lambda$ blocks. We estimate the minimal number of blocks of $\lambda$-regular orthomodular lattices to be lower than of equal to $\lambda^2$ regardless of $k$. (English) |
| Keyword:
|
Greechie diagram |
| Keyword:
|
finite orthomodular lattice |
| Keyword:
|
maximal Boolean subalgebra |
| MSC:
|
03G12 |
| MSC:
|
05C65 |
| MSC:
|
06C15 |
| idZBL:
|
Zbl 0689.06008 |
| idMR:
|
MR1026509 |
| DOI:
|
10.21136/AM.1989.104375 |
| . |
| Date available:
|
2008-05-20T18:37:52Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104375 |
| . |
| Reference:
|
[1] M. Dichtl: Astroids and pastings.Algebra Universalis 18 (1984), 380-385. Zbl 0546.06007, MR 0745498, 10.1007/BF01203371 |
| Reference:
|
[2] R. J. Greechie: Orthomodular lattices admitting no states.J. Combinatorial Theory 10 (1971), 119-132. Zbl 0219.06007, MR 0274355, 10.1016/0097-3165(71)90015-X |
| Reference:
|
[3] G. Kalmbach: Orthomodular Lattices.Academic Press, London, 1984. Zbl 0538.06009, MR 0716496 |
| Reference:
|
[4] E. Köhler: Orthomodulare Verbände rnit Regularitätsbedingungen.J. of Geometry 119 (1982), 130-145. MR 0695705, 10.1007/BF01930874 |
| Reference:
|
[5] M. Navara V. Rogalewicz: The pasting constructions for Orthomodular posets.Submitted for publication. |
| Reference:
|
[6] V. Rogalewicz: Any orthomodular poset is a pasting of Boolean algebras.Comment. Math. Univ. Carol. 29 (1988), 557-558. Zbl 0659.06006, MR 0972837 |
| . |
