# Definition:Group of Units/Ring

## Definition

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

Then the set $U_R$ of units of $\struct {R, +, \circ}$ is called the group of units of $\struct {R, +, \circ}$.

This can be denoted explicitly as $\struct {U_R, \circ}$.

## Also denoted as

The group of units of a ring with unity $R$ is also seen denoted as $R^\times$, or explicitly as $\struct {R^\times, \circ}$.