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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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          Author and article information

          Journal
          22 May 2015
          2015-05-27
          Article
          1505.06224

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          20N05, 39B52, 08A05
          9 pages
          math.RA

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