| Title:
|
A geometric approach to universal quasigroup identities (English) |
| Author:
|
Havel, V. J. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
97-103 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we construct the accompanying identity $\hat{I}$ of a given quasigroup identity $I$. After that we deduce the main result: $I$ is isotopically invariant (i.e., for every guasigroup $Q$ it holds that if $I$ is satisfied in $Q$ then $I$ is satisfied in every quasigroup isotopic to $Q$) if and only if it is equivalent to $\hat{I}$ (i.e., for every quasigroup $Q$ it holds that in $Q$ either $I, \hat{I}$ are both satisfied or both not). (English) |
| Keyword:
|
3-webs and their coordinatizing quasigroups |
| Keyword:
|
isotopic quasigroups and loops |
| Keyword:
|
identities invariant under isotopies |
| Keyword:
|
accompanying identities |
| MSC:
|
05B30 |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 0797.05025 |
| idMR:
|
MR1242632 |
| . |
| Date available:
|
2008-06-06T21:24:06Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107470 |
| . |
| Reference:
|
[1] Brožíková, E.: On universal quasigroup identities.Mathematica Bohemica 117 (1992), 20-32. MR 1154051 |
| Reference:
|
[2] Evans, T.: Identical relation in loops, I.Journ. Austral. Math. Soc. 12 (1971), 275-286. MR 0297915 |
| Reference:
|
[3] Falconer, E.: Isotopy invariants in quasigroups.Trans. Amer. Math. Soc. 151 (1970), 511-526. Zbl 0209.04701, MR 0272932 |
| Reference:
|
[4] Movsisjan, J. M.: Introduction to the theory of algebras with hyperidentities.(in Russian), Erevan, 1986. MR 0877518 |
| Reference:
|
[5] Belousov, V. D."$^\dag $"V. D. Belousov ($^\ast $20.2.1925, $^\dag $23.7.1988) was a leader of the Russian research in quasigroup theory.: Algebraic nets and quasigroups.(in Russian), Kishinev, 1971. |
| . |
