Definition:Quasigroup/Right Quasigroup

Definition
Let $\struct {S, \circ}$ be a magma.

$\struct {S, \circ}$ is a right quasigroup :
 * for all $a \in S$, the right regular representation $\rho_a$ is a permutation on $S$.

That is:
 * $\forall a, b \in S: \exists ! x: x \circ a = b$

Also see

 * Definition:Left Quasigroup