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Quasigroup
Definition
| $X$ |
| $ \langle X,* \rangle \in \text{Quasigroup}(X)$ |
| $*\in \mathrm{magma}(X)$ |
| $a,b,x,y\in X$ |
| $ \forall a.\ \forall b.\ \exists x.\ a*x=b $ |
| $ \forall a.\ \forall b.\ \exists y.\ y*a=b $ |
Here we used infix notation for “$*$”.
Ramifications
Discussion
The binary operation is often called multiplication.
The axioms $*\in \mathrm{binaryOp}(X)$ above means that a monoid is closed with respect to the multiplication.
One generally calls $X$ the quasigroup, i.e. the set where the operation “$*$” is defined on.
Reference
Wikipedia: Quasigroup
Context
Subset of
