Geodesic
On the lattices of quasivarieties of differential groupoids
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 11-17 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 08C15, 20N02
Keywords: mode; differential groupoid; lattice of subquasivarieties; $\Cal Q$-universal quasivariety 
@article{CMUC_2008_49_1_a1,
     author = {Kravchenko, A. V.},
     title = {On the lattices of quasivarieties of differential groupoids},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {11--17},
     year = {2008},
     volume = {49},
     number = {1},
     mrnumber = {2432816},
     zbl = {1212.08005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2008_49_1_a1/}
}
TY  - JOUR
AU  - Kravchenko, A. V.
TI  - On the lattices of quasivarieties of differential groupoids
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2008
SP  - 11
EP  - 17
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMUC_2008_49_1_a1/
LA  - en
ID  - CMUC_2008_49_1_a1
ER  - 
%0 Journal Article
%A Kravchenko, A. V.
%T On the lattices of quasivarieties of differential groupoids
%J Commentationes Mathematicae Universitatis Carolinae
%D 2008
%P 11-17
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/CMUC_2008_49_1_a1/
%G en
%F CMUC_2008_49_1_a1
Kravchenko, A. V. On the lattices of quasivarieties of differential groupoids. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 11-17. http://geodesic.mathdoc.fr/item/CMUC_2008_49_1_a1/