| Title:
|
Valuations on modular lattices (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
391-395 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is well-known that there exist infinite modular lattices possessing no non-trivial valuations. In this paper a class $\Cal K$ of modular lattices is defined and it is proved that each lattice belonging to $\Cal K$ has a nontrivial valuation. Next, a result of $G$. Birkhoff concerning valuations on modular lattices of finite length is generalized. (English) |
| Keyword:
|
modular lattices |
| Keyword:
|
prime quotients |
| Keyword:
|
order-dense quotients |
| Keyword:
|
valuation |
| Keyword:
|
discrete valuation |
| MSC:
|
06C05 |
| idZBL:
|
Zbl 0753.06008 |
| idMR:
|
MR1146397 |
| DOI:
|
10.21136/MB.1991.126021 |
| . |
| Date available:
|
2009-09-24T20:47:40Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126021 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory.Providence 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[2] G. Grätzer: General Lattice Theory.Akademie Verlag, Berlin, 1978. MR 0504338 |
| Reference:
|
[3] B. Monjardet: Metrics on partially ordered sets - a survey.Discrete Math. 35 (1981), 173-184. Zbl 0463.46016, MR 0620670, 10.1016/0012-365X(81)90206-5 |
| Reference:
|
[4] E. T. Schmidt: Über die Kongruenzverbände der Verbände.Publ. Math. Debrecen 9 (1962), 245-256. Zbl 0178.33902, MR 0151405 |
| . |
