Definition:Quasigroup/Right Quasigroup

Definition
Let $\left({S, \circ}\right)$ be a magma.

$\left({S, \circ}\right)$ is a right quasigroup iff:
 * for all $a \in S$, the right regular representation $\rho_a$ is a permutations on $S$.

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

Also see

 * Definition:Left Quasigroup