Definition:Group of Units

Theorem
Let $\left({R, +, \circ}\right)$ be a ring with unity.

Then the set $U_R$ of units of $\left({R, +, \circ}\right)$ forms a group under $\circ$.

This group $\left({U_R, \circ}\right)$ is called the group of units of the ring.

Proof
This follows directly from Invertible Elements of Monoid form Subgroup.

Also known as
The group of units of a ring with unity $R$ is also seen denoted as $R^\times$.