| Title:
|
A note on convex sublattices of lattices (English) |
| Author:
|
Slavík, Václav |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
7-9 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $CSub\,(\text{\bf K})$ denote the variety of lattices generated by convex sublattices of lattices in $\text{\bf K}$. For any proper variety $\text{\bf V}$, the variety $CSub\,(\text{\bf V})$ is proper. There are uncountably many varieties $\text{\bf V}$ with $CSub\,(\text{\bf V})=\text{\bf V}$. (English) |
| Keyword:
|
lattice |
| Keyword:
|
convex sublattice |
| Keyword:
|
variety |
| MSC:
|
06B20 |
| MSC:
|
06B25 |
| idZBL:
|
Zbl 0821.06007 |
| idMR:
|
MR1334407 |
| . |
| Date available:
|
2009-01-08T18:15:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118725 |
| . |
| Reference:
|
[1] Grätzer G.: General Lattice Theory.Birkhäuser Verlag, 1978. MR 0504338 |
| Reference:
|
[2] Adams M.E., Sichler J.: Lattices with unique complementation.Pacif. J. Math. 92 (1981), 1-13. Zbl 0468.06005, MR 0618040 |
| Reference:
|
[3] McKenzie R.: Equational bases for lattice theories.Math. Scand. 27 (1970), 24-38. Zbl 0307.08001, MR 0274353 |
| Reference:
|
[4] Wille R.: Primitive subsets of lattices.Alg. Universalis 2 (1972), 95-98. Zbl 0269.06001, MR 0311524 |
| . |
