| Title:
|
Complemented ordered sets (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
28 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
25-34 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the concept of complementary elements in ordered sets. If an ordered set $S$ is a lattice, this concept coincides with that for lattices. The connections between distributivity and the uniqueness of complements are shown and it is also shown that modular complemented ordered sets represents “geometries” which are more general than projective planes. (English) |
| Keyword:
|
modular ordered set |
| Keyword:
|
distributive ordered set |
| Keyword:
|
complemented ordered set |
| Keyword:
|
projective plane |
| MSC:
|
06A06 |
| idZBL:
|
Zbl 0785.06002 |
| idMR:
|
MR1201863 |
| . |
| Date available:
|
2008-06-06T21:04:38Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107433 |
| . |
| Reference:
|
[1] Birkhoff G.: Lattice Theory.Amer. Math. Soc. Colloq. Publ. 25 (1967), N.Y., (3-rd edition). Zbl 0153.02501, MR 0227053 |
| Reference:
|
[2] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets.Order 5 (1989), 407 – 423. MR 1010389 |
| Reference:
|
[3] Grätzer G.: General Lattice Theory.Basel, Stuttgart, 1978. MR 0509213 |
| Reference:
|
[4] Larmerová J., Rachůnek J.: Translations of distributive and modular ordered sets.Acta Univ. Palack. (to appear), Olomouc. |
| Reference:
|
[5] Pierce G.S.: On the algebra of logic.Amer. J. Math. (1980), 15 – 57. |
| Reference:
|
[6] Rachůnek J.: Translations des ensembles ordonés.Math. Slovaca 31 (1981), 337 – 340. MR 0637961 |
| Reference:
|
[7] Salij V.N.: Uniquely complemented lattices.Nauka, Moskva, 1984, (in Russian). |
| . |
