# Multiary semigroup

From Groupprops

## Definition

A **multiary semigroup**, also called a **polyadic semigroup**, is a -ary semigroup for some . Note that the case corresponds to the usual notion of semigroup.

A -ary semigroup is defined as a set with a -ary operation, i.e., a map such that all different ways of associating expressions involving the -ary operation yield equivalent results. Note that this boils down to checking that all the distinct possible ways of associating an expression of length give the same answer.

## Related notions

- Multiary quasigroup
- Multiary group is something that is both a multiary semigroup and a multiary quasigroup.