Definition:Cancellable Element/Left Cancellable

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

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

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

Also known as

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

Hence the property of being cancellable is also referred to 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 cancellability can be found here.