Strictly quadratic functional equations on quasigroups. I.

Krapez, A.

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Parastrophically Equivalent Quasigroup Equations

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On Solving A System Of Balanced Functional Equations Of Quaigroups III

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On a system of functional equations on quasigroups.

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Solution of distributive-like quasigroup functional equations

Fedir M. Sokhatsky, Halyna V. Krainichuk (2012)

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We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like...

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Invertibility criterion of composition of two multiary quasigroups

Fedir M. Sokhatsky, Iryna V. Fryz (2012)

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We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for $T$ -quasigroups. For this purpose we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [Belyavskaya G., Mullen G.L.: Orthogonal hypercubes and $n$ -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We...