| Title:
|
On the lattices of quasivarieties of differential groupoids (English) |
| Author:
|
Kravchenko, A. V. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
11-17 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main result of Romanowska A., Roszkowska B., {\it On some groupoid modes\/}, Demonstratio Math. {\bf 20} (1987), no. 1--2, 277--290, provides us with an explicit description of the lattice of varieties of differential groupoids. In the present article, we show that this variety is $\Cal Q$-universal, which means that there is no convenient explicit description for the lattice of quasivarieties of differential groupoids. We also find an example of a subvariety of differential groupoids with a finite number of subquasivarieties. (English) |
| Keyword:
|
mode |
| Keyword:
|
differential groupoid |
| Keyword:
|
lattice of subquasivarieties |
| Keyword:
|
$\Cal Q$-universal quasivariety |
| MSC:
|
08C15 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 1212.08005 |
| idMR:
|
MR2432816 |
| . |
| Date available:
|
2009-05-05T17:06:06Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119697 |
| . |
| Reference:
|
[1] Adams M.E., Adaricheva K.V., Dziobiak W., Kravchenko A.V.: Open problems related to the problem of Birkhoff and Maltsev.Studia Logica 78 (2004), 357-378. MR 2108035 |
| Reference:
|
[2] Gorbunov V.A.: Algebraic Theory of Quasivarieties.Plenum New York-London-Moscow (1998). Zbl 0986.08001, MR 1654844 |
| Reference:
|
[3] Ježek J., Kepka T.: Medial groupoids.Rozpravy Československé Akad. Věd, Řada Mat. Přírod. Věd 93 (1983), 2. MR 0734873 |
| Reference:
|
[4] Płonka J.: On $k$-cyclic groupoids.Math. Japon. 30 (1985), 3 371-382. MR 0803288 |
| Reference:
|
[5] Romanowska A.: On some representations of groupoid modes satisfying the reduction law.Demonstratio Math. 21 (1988), 4 943-960. Zbl 0677.20057, MR 0993839 |
| Reference:
|
[6] Romanowska A., Roszkowska B.: On some groupoid modes.Demonstratio Math. 20 (1987), 1-2 277-290. Zbl 0669.08005, MR 0941422 |
| Reference:
|
[7] Romanowska A., Roszkowska B.: Representation of $n$-cyclic groupoids.Algebra Universalis 26 (1989), 1 7-15. MR 0981422, 10.1007/BF01243869 |
| Reference:
|
[8] Romanowska A.B., Smith J.D.H.: Differential groupoids.Contributions to General Algebra 7 Proc. Vienna Conf. (Vienna, 1990) 283-290 Teubner Stuttgart (1991). Zbl 0744.20055, MR 1143092 |
| Reference:
|
[9] Romanowska A.B., Smith J.D.H.: Modes.World Scientific Singapore (2002). Zbl 1012.08001, MR 1932199 |
| . |
