# Article

 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). 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. .

## Files

Files Size Format View
ArchMathRetro_029-1993-1_12.pdf 237.3Kb application/pdf View/Open

Partner of