Multiary quasigroup

Definition

A multiary quasigroup or polyadic quasigroup is a $n$ -ary quasigroup for some $n \geq 2$ . 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 <mah>a_j</math>s and $b$ ) known.

Related notions

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