Medial quasigroups of type $(n,k)$

Alena Vanžurová

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$m$ -medial $n$ -quasigroups

Tomáš Kepka (1991)

Commentationes Mathematicae Universitatis Carolinae

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For $n \geq 4$ , every $n$ -medial $n$ -quasigroup is medial. If $1 \leq m < n$ , then there exist $m$ -medial $n$ -quasigroups which are not $(m + 1)$ -medial.

Golden section quasigroups as special idempotent medial quasigroups

Václav Havel, Miloslava Sedlářová (1994)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A geometric approach to universal quasigroup identities

Václav J. Havel (1993)

Archivum Mathematicum

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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).

Displaying similar documents to “Medial quasigroups of type ( n , k ) ”

m -medial n -quasigroups

Golden section quasigroups as special idempotent medial quasigroups

A geometric approach to universal quasigroup identities

Displaying similar documents to “Medial quasigroups of type $(n, k)$ ”

$m$ -medial $n$ -quasigroups