# Invertible Element of Associative Structure is Cancellable/Corollary

< Invertible Element of Associative Structure is Cancellable(Redirected from Invertible Element of Monoid is Cancellable)

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## Theorem

Let $\struct {S, \circ}$ be a monoid whose identity element is $e_S$.

An element of $\struct {S, \circ}$ which is invertible is also cancellable.

## Proof

By definition, a monoid is an associative algebraic structure with an identity element.

The result follows from Invertible Element of Associative Structure is Cancellable.

$\blacksquare$