Multiary quasigroup

Definition
A multiary quasigroup or polyadic quasigroup is a $$n$$-ary quasigroup for some $$n \ge 2$$. Note that the $$n = 2$$ case corresponds to the usual notion of quasigroup.

A $$n$$-ary quasigroup is defined as a set $$G$$ with a $$n$$-ary operation, i.e., a map $$f: G^n \to G$$ such that the equation $$f(a_1,a_2,\dots,a_n) = b$$ has a unique solution with any $$a_i$$ as the unknown and all other quantities (i.e., all the other a_j s and $$b$$) known.

Related notions

 * Multiary semigroup
 * Multiary group is something that's both a multiary quasigroup and a multiary semigroup