Havel, V. J. A geometric approach to universal quasigroup identities. (English) Zbl 0797.05025 Arch. Math., Brno 29, No. 1-2, 97-103 (1993). Summary: We construct the accompanying identity \(\widehat{\mathcal I}\) of a given quasigroup identity \({\mathcal I}\). After that we deduce the main result: \({\mathcal I}\) is isotopically invariant (i.e., for every quasigroup \({\mathbb{Q}}\) it holds that if \({\mathcal I}\) is satisfied in \({\mathbb{Q}}\) then \({\mathcal I}\) is satisfied in every quasigroup isotopic to \({\mathbb{Q}}\)) if and only if it is equivalent to \(\widehat{\mathcal I}\) (i.e., for every quasigroup \({\mathbb{Q}}\) it holds that in \({\mathbb{Q}}\) either \({\mathcal I}\), \(\widehat{\mathcal I}\) are both satisfied or both not). MSC: 05B30 Other designs, configurations 20N05 Loops, quasigroups Keywords:3-webs; coordinatizing quasigroups; isotopic quasigroups; accompanying identity; quasigroup identity; isotopically invariant × Cite Format Result Cite Review PDF Full Text: EuDML EMIS