| Title:
|
Join-closed and meet-closed subsets in complete lattices (English) |
| Author:
|
Machala, František |
| Author:
|
Slezák, Vladimír |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
113-117 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
To every subset $A$ of a complete lattice $L$ we assign subsets $J(A)$, $M(A)$ and define join-closed and meet-closed sets in $L$. Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper. (English) |
| Keyword:
|
complete lattices |
| Keyword:
|
join-closed and meet-closed sets |
| MSC:
|
06B23 |
| MSC:
|
08A02 |
| MSC:
|
08A05 |
| idZBL:
|
Zbl 1085.06003 |
| idMR:
|
MR2124608 |
| . |
| Date available:
|
2009-08-21T12:54:41Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132940 |
| . |
| Reference:
|
[1] Crawley P., Dilworth R. P.: Algebraic Theory of Lattices. : Englewood Cliffs., 1973. |
| Reference:
|
[2] Czédli G., Huhn A. P., Schmidt E. T.: Weakly independent sets in lattices.Algebra Univers. 20 (1985), 194–196. MR 0806613 |
| Reference:
|
[3] Dlab V.: Lattice formulation of general algebraic dependence.Czech. Math. Journal 20, 95 (1970), 603–615. Zbl 0247.06006, MR 0268093 |
| Reference:
|
[4] Grätzer G.: General Lattice Theory. : Birkhäuser Verlag., 1998. MR 1670580 |
| Reference:
|
[5] Machala F.: Join-independent and meet-independent sets in complete lattices.Order 18 (2001), 269–274. Zbl 1009.06005, MR 1867237 |
| Reference:
|
[6] Machala F., Slezák V.: Lattice-inadmissible incidence structures.Discuss. Math. (submitted). Zbl 1073.06004 |
| Reference:
|
[7] Slezák V.: On the special context of independent sets.Discuss. Math., Gen. Algebra and Appl. 21 (2001), 115–122. Zbl 0997.06003, MR 1868622 |
| Reference:
|
[8] Szász G.: Introduction to Lattice Theory. : Akadémiai Kiadó., Budapest, 1963. MR 0166118 |
| . |
