nLab commutative quasigroup

Contents

Contents

Definition

A commutative quasigroup is a commutative magma (G,()():G×GG)(G,(-)\cdot(-):G \times G \to G) equipped with a binary operation ()/():G×GG(-)/(-):G \times G \to G called division such that (x/y)y=x(x/y) \cdot y = x and (xy)/y=x(x \cdot y)/y = x.

Examples

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