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      Algebras with Medial-like Functional Equations on Quasigroups

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          Abstract

          We consider \(14\) medial-like balanced functional equations with four object variables for a pair \((f, g)\) of binary quasigroup operations. Then, we prove that every algebra \((B; f, g)\) with quasigroup operations satisfying a medial-like balanced functional equation has a linear representation on an abelian group \((B; +)\).

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          Journal
          1505.06224

          Algebra

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