# Group of Units is Group

## Theorem

Let $\struct {R, +, \circ}$ be a ring with unity.

Then the set of units of $\struct {R, +, \circ}$ forms a group under $\circ$.

Hence the justification for referring to the group of units of $\struct {R, +, \circ}$.

## Proof

Follows directly from Invertible Elements of Monoid form Subgroup of Cancellable Elements.

$\blacksquare$