Definition:Quasigroup/Right Quasigroup

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

$\struct {S, \circ}$ is a right quasigroup if and only if:

for all $a \in S$, the right regular representation $\rho_a$ is a permutation on $S$.

That is:

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

Also see

  • Results about quasigroups can be found here.