nLab n-ary semigroup

Idea

A generalization of semigroup to n-ary operations.

Definition

Given a natural number $n$, an $n$-ary semigroup is a set $S$ with an $n$-ary operation $f:S^n \to S$, such that every one of the $n$ possible bracketings of a list consisting of $2n - 1$ distinct elements with any $n$ consecutive elements bracketed are equal to each other.

See also

• semigroup

• n-ary magma

• n-ary quasigroup

• n-ary group

References

• Wikipedia, n-ary group