# semigroup

> English word · Noun · frequency rank #89,884

## Definitions
1. Any set for which there is a binary operation that is closed and associative.

## Etymology
From semi- + group, reflecting the fact that not all the conditions required for a group are required for a semigroup. (Specifically, the requirements for the existence of identity and inverse elements are omitted.)

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/semigroup