| Title:
|
A decomposition of homomorphic images of nearlattices (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Kolařík, Miroslav |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
43-51 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice $\mathcal{S}$ and its element $c$ the mapping $\varphi _c(x) = \langle x \vee c, x \wedge _p c \rangle $ is a (surjective, injective) homomorphism of $\mathcal{S}$ into $[c) \times (c]$. (English) |
| Keyword:
|
nearlattice |
| Keyword:
|
semilattice |
| Keyword:
|
distributive element |
| Keyword:
|
pseudocomplement |
| Keyword:
|
dual pseudocomplement |
| MSC:
|
06A12 |
| MSC:
|
06B99 |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 1123.06002 |
| idMR:
|
MR2321296 |
| . |
| Date available:
|
2009-08-21T07:04:06Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133440 |
| . |
| Reference:
|
[1] Chajda I., Kolařík M.: Nearlattices.Discrete Math., submitted. Zbl 1151.06004, MR 2446101 |
| Reference:
|
[2] Cornish W. H.: The free implicative BCK-extension of a distributive nearlattice.Math. Japonica 27, 3 (1982), 279–286. Zbl 0496.03046, MR 0663155 |
| Reference:
|
[3] Cornish W. H., Noor A. S. A.: Standard elements in a nearlattice.Bull. Austral. Math. Soc. 26, 2 (1982), 185–213. Zbl 0523.06006, MR 0683652 |
| Reference:
|
[4] Grätzer G.: General Lattice Theory. : Birkhäuser Verlag, Basel., 1978. MR 0504338 |
| Reference:
|
[5] Noor A. S. A., Cornish W. H.: Multipliers on a nearlattices.Comment. Math. Univ. Carol. (1986), 815–827. MR 0874675 |
| Reference:
|
[6] Scholander M.: Trees, lattices, order and betweenness.Proc. Amer. Math. Soc. 3 (1952), 369–381. MR 0048405 |
| Reference:
|
[7] Scholander M.: Medians and betweenness.Proc. Amer. Math. Soc. 5 (1954), 801–807. MR 0064749 |
| Reference:
|
[8] Scholander M.: Medians, lattices and trees.Proc. Amer. Math. Soc. 5 (1954), 808–812. MR 0064750 |
| . |
