# Cancellative semigroup

From Groupprops

This article defines a semigroup property: a property that can be evaluated to true/false for any given semigroup

View a complete list of semigroup properties

## Definition

### Symbol-free definition

A **cancellative semigroup** (also called **cancellation semigroup**) is a semigroup where every element is cancellative.

### Definition with symbols

A semigroup (a set with associative binary operation ) if the following hold for all :