| Title:
|
Lattices and semilattices having an antitone involution in every upper interval (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
577-585 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study $\vee$-semilat\/tices and lat\/tices with the greatest element 1 where every interval [p,1] is a lat\/tice with an antitone involution. We characterize these semilat\/tices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilat\/tices or lat\/tices form varieties. The congruence properties of these varieties are investigated. (English) |
| Keyword:
|
semilat\/tice |
| Keyword:
|
lat\/tice |
| Keyword:
|
antitone involution |
| Keyword:
|
congruence permutability |
| Keyword:
|
weak regularity |
| MSC:
|
06A12 |
| MSC:
|
06C15 |
| MSC:
|
06F35 |
| MSC:
|
08B05 |
| MSC:
|
08B10 |
| idZBL:
|
Zbl 1101.06003 |
| idMR:
|
MR2062874 |
| . |
| Date available:
|
2009-01-08T19:31:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119412 |
| . |
| Reference:
|
[1] Abbott J.C.: Semi-boolean algebras.Matem. Vestnik 4 (1967), 177-198. MR 0239957 |
| Reference:
|
[2] Burris S., Sankappanavar H.P.: A Course in Universal Algebra.Springer-Verlag, 1981. Zbl 0478.08001, MR 0648287 |
| Reference:
|
[3] Chajda I.: An extension of relative pseudocomplementation to non-distributive lattices.Acta Sci. Math. (Szeged), to appear. Zbl 1048.06005, MR 2034188 |
| Reference:
|
[4] Chajda I., Halaš R., Länger H.: Orthomodular implication algebras.Internat. J. Theoret. Phys. 40 (2001), 1875-1884. Zbl 0992.06008, MR 1860644 |
| Reference:
|
[5] Csakany B.: Characterizations of regular varieties.Acta Sci. Math. (Szeged) 31 (1970), 187-189. Zbl 0216.03302, MR 0272697 |
| Reference:
|
[6] Werner H.: A Mal'cev condition on admissible relations.Algebra Universalis 3 (1973), 263. MR 0330009 |
| . |
