Geodesic
Some regular quasivarieties of commutative binary modes
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 471-484.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Irregular (quasi)varieties of groupoids are (quasi)varieties that do not contain semilattices. The regularization of a (strongly) irregular variety $\mathcal{V}$ of groupoids is the smallest variety containing $\mathcal{V}$ and the variety $\mathcal{S}$ of semilattices. Its quasiregularization is the smallest quasivariety containing $\mathcal{V}$ and $\mathcal{S}$. In an earlier paper the authors described the lattice of quasivarieties of cancellative commutative binary modes, i.e. idempotent commutative and entropic (or medial) groupoids. They are all irregular and the lattice contains all irregular varieties of such groupoids. This paper extends the earlier result, by investigating some regular quasivarieties. It provides a full description of the lattice of subquasivarieties of the regularization of any irregular variety of commutative binary modes.
Classification : 08A62, 08C15, 20N02, 20N05
Keywords: regular quasivarieties; regular quasi-identity; modes; affine spaces; commutative binary modes 
@article{CMUC_2014__55_4_a3,
     author = {Matczak, K. and Romanowska, A. B.},
     title = {Some regular quasivarieties of commutative binary modes},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {471--484},
     publisher = {mathdoc},
     volume = {55},
     number = {4},
     year = {2014},
     mrnumber = {3269009},
     zbl = {06391555},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a3/}
}
TY  - JOUR
AU  - Matczak, K.
AU  - Romanowska, A. B.
TI  - Some regular quasivarieties of commutative binary modes
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2014
SP  - 471
EP  - 484
VL  - 55
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a3/
LA  - en
ID  - CMUC_2014__55_4_a3
ER  - 
%0 Journal Article
%A Matczak, K.
%A Romanowska, A. B.
%T Some regular quasivarieties of commutative binary modes
%J Commentationes Mathematicae Universitatis Carolinae
%D 2014
%P 471-484
%V 55
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a3/
%G en
%F CMUC_2014__55_4_a3
Matczak, K.; Romanowska, A. B. Some regular quasivarieties of commutative binary modes. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 4, pp. 471-484. http://geodesic.mathdoc.fr/item/CMUC_2014__55_4_a3/