| Title:
|
Natural extension of a congruence of a lattice to its lattice of convex sublattices (English) |
| Author:
|
Bhatta, S. Parameshwara |
| Author:
|
Ramananda, H. S. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
133-138 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $L$ be a lattice. In this paper, corresponding to a given congruence relation $\Theta $ of $L$, a congruence relation $\Psi _\Theta $ on $CS(L)$ is defined and it is proved that
1.
$CS(L/\Theta )$ is isomorphic to $CS(L)/\Psi _\Theta $;
2.
$L/\Theta $ and $CS(L)/\Psi _\Theta $ are in the same equational class;
3.
if $\Theta $ is representable in $L$, then so is $\Psi _\Theta $ in $CS(L)$. (English) |
| Keyword:
|
lattice of convex sublattices of a lattice |
| Keyword:
|
congruence relation |
| Keyword:
|
representable congruence relation |
| MSC:
|
06B10 |
| MSC:
|
06B20 |
| idZBL:
|
Zbl 1249.06007 |
| idMR:
|
MR2813539 |
| . |
| Date available:
|
2011-06-06T14:42:36Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141562 |
| . |
| Reference:
|
[1] Grätzer, G.: General Lattice Theory.2nd ed., Birkhäuser Verlag, 1998. MR 1670580 |
| Reference:
|
[2] Grätzer, G.: The Congruence of a Finite Lattice, A Proof by Picture Aproach.Birkhäuser Boston, 2006. MR 2177459 |
| Reference:
|
[3] Lavanya, S., Parameshwara Bhatta, S.: A new approach to the lattice of convex sublattice of a lattice.Algebra Universalis 35 (1996), 63–71. MR 1360531, 10.1007/BF01190969 |
| Reference:
|
[4] Parameshwara Bhatta, S., Ramananda, H. S.: On ideals and congruence relations in trellises.Acta Math. Univ. Comenian. 2 (2010), 209–216. MR 2745169 |
| . |
