# nLab n-ary semigroup

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## 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.