Quasigroup covers of division groupoids
Jaroslav J. Ježek; Tomáš Kepka; Petr Němec
Commentationes Mathematicae Universitatis Carolinae (2023)
- Volume: 64, Issue: 3, page 265-278
- ISSN: 0010-2628
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topJežek, Jaroslav J., Kepka, Tomáš, and Němec, Petr. "Quasigroup covers of division groupoids." Commentationes Mathematicae Universitatis Carolinae 64.3 (2023): 265-278. <http://eudml.org/doc/299226>.
@article{Ježek2023,
abstract = {Let $G$ be a division groupoid that is not a quasigroup. For each regular cardinal $\alpha >|G|$ we construct a quasigroup $Q$ on $G\times \alpha $ that is a quasigroup cover of $G$ (i.e., $G$ is a homomorphic image of $Q$ and $G$ is not an image of any quasigroup that is a proper factor of $Q$). We also show how to easily obtain quasigroup covers from free quasigroups.},
author = {Ježek, Jaroslav J., Kepka, Tomáš, Němec, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {groupoid; division; quasigroup; cover},
language = {eng},
number = {3},
pages = {265-278},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quasigroup covers of division groupoids},
url = {http://eudml.org/doc/299226},
volume = {64},
year = {2023},
}
TY - JOUR
AU - Ježek, Jaroslav J.
AU - Kepka, Tomáš
AU - Němec, Petr
TI - Quasigroup covers of division groupoids
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 3
SP - 265
EP - 278
AB - Let $G$ be a division groupoid that is not a quasigroup. For each regular cardinal $\alpha >|G|$ we construct a quasigroup $Q$ on $G\times \alpha $ that is a quasigroup cover of $G$ (i.e., $G$ is a homomorphic image of $Q$ and $G$ is not an image of any quasigroup that is a proper factor of $Q$). We also show how to easily obtain quasigroup covers from free quasigroups.
LA - eng
KW - groupoid; division; quasigroup; cover
UR - http://eudml.org/doc/299226
ER -
References
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