# Definition:Cancellable Element/Right Cancellable

## Definition

Let $\struct {S, \circ}$ be an algebraic structure.

An element $x \in \struct {S, \circ}$ is right cancellable if and only if:

$\forall a, b \in S: a \circ x = b \circ x \implies a = b$

## Also known as

An object that is cancellable can also be referred to as cancellative.

Hence the property of being cancellable is given on $\mathsf{Pr} \infty \mathsf{fWiki}$ as cancellativity.

Some authors use regular to mean cancellable, but this usage can be ambiguous so is not generally endorsed.

## Also see

• Results about cancellativity can be found here.