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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