Geodesic
A geometric approach to universal quasigroup identities
Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 97-103
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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).
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).
Classification : 05B30, 20N05
Keywords: 3-webs and their coordinatizing quasigroups; isotopic quasigroups and loops; identities invariant under isotopies; accompanying identities 
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     title = {A geometric approach to universal quasigroup identities},
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     pages = {97--103},
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     url = {http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a11/}
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Havel, V. J. A geometric approach to universal quasigroup identities. Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 97-103. http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a11/

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