# Definition:Group of Units/Ring

< Definition:Group of Units(Redirected from Definition:Group of Units of Ring)

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## 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 $\struct {R^\times, \circ}$.