Cancellative semigroup

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 $(S,*)$ (a set $S$ with associative binary operation $*$) if the following hold for all $a,b,c\in S$:

• $a*b=a*c\implies b=c$
• $b*a=c*a\implies b=c$