Article
| Title: | Quasigroup covers of division groupoids (English) |
| Author: | Ježek, Jaroslav J. |
| Author: | Kepka, Tomáš J. |
| Author: | Němec, Petr C. |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 265-278 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | groupoid |
| Keyword: | division |
| Keyword: | quasigroup |
| Keyword: | cover |
| MSC: | 20N05 |
| DOI: | 10.14712/1213-7243.2024.002 |
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| Date available: | 2024-03-18T10:34:32Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152297 |
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