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 |
| . | |
| Category: | math |
| . | |
| 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 |
| idZBL: | Zbl 07830508 |
| idMR: | MR4717501 |
| DOI: | 10.14712/1213-7243.2024.002 |
| . | |
| Date available: | 2024-03-18T10:34:32Z |
| Last updated: | 2024-08-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152297 |
| . | |
| Reference: | [1] Albert A. A.: Qusigroups. I.Trans. Amer. Math. Soc. 54 (1943), 507–519. MR 0009962, 10.1090/S0002-9947-1943-0009962-7 |
| Reference: | [2] Baer R.: The homomorphism theorems for loops.Amer. J. Math. 67 (1945), 458–460. Zbl 0063.00166, MR 0012302, 10.2307/2371960 |
| Reference: | [3] Bates G. E., Kiokemeister F.: A note on homomorphic mapping of quasigroups into multiplicative systems.Bull. Amer. Math. Soc. 54 (1948), 1180–1185. MR 0027768, 10.1090/S0002-9904-1948-09146-7 |
| Reference: | [4] Bruck R. H.: Simple quasigroups.Bull. Amer. Math. Soc. 50 (1944), 769–781. MR 0011311, 10.1090/S0002-9904-1944-08236-0 |
| Reference: | [5] Bruck R. H.: Some results in the theory of linear non-associative algebras.Trans. Amer. Math. Soc. 56 (1944), 141–199. MR 0011083, 10.1090/S0002-9947-1944-0011083-5 |
| Reference: | [6] Bruck R. H.: A Survey of Binary Systems.Gruppentheorie, Ergebnisse der Mathematik und ihre Grenzgebiete, (N.F.), 20, Springer, Berlin, 1958. Zbl 0141.01401, MR 0093552 |
| Reference: | [7] Evans T.: On multiplicative systems defined by generators and relations. I. Normal form theorems.Proc. Cambridge Philos. Soc. 47 (1951), 637–649. MR 0043764 |
| Reference: | [8] Garrison G. N.: Quasi-groups.Ann. of Math. (2) 41 (1940), 474–487. MR 0002150 |
| Reference: | [9] Hausmann B. A., Ore O.: Theory of quasi-groups.Amer. J. Math. 59 (1937), no. 4, 983–1004. MR 1507296, 10.2307/2371362 |
| Reference: | [10] Kepka T., Němec P.: In memory of Jaroslav Ježek.Acta Univ. Carolin. Math. Phys. 53 (2012), no. 2, 3–4. MR 3099636 |
| Reference: | [11] Kiokemeister F.: A theory of normality for quasigroups.Amer. J. Math. 70 (1948), 99–106. MR 0023252, 10.2307/2371934 |
| . |
Fulltext not available (moving wall 24 months)
Search
Partner of
