Group is Cancellable Monoid
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Theorem
Let $\struct {G, \circ}$ be a group.
Then $\struct {G, \circ}$ is a cancellable monoid.
Proof
By definition, a group is a fortiori a monoid.
From Group Operation is Cancellable, $\circ$ is a cancellable operation in $G$.
Hence the result by definition of cancellable monoid.
$\blacksquare$
Sources
- 1999: J.C. Rosales and P.A. García-Sánchez: Finitely Generated Commutative Monoids ... (previous) ... (next): Chapter $1$: Basic Definitions and Results