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