Definition:Group of Units
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Definition
Group of Units of Monoid
Let $\struct {S, \circ}$ be a monoid.
Then the set $U_S$ of invertible elements of $\struct {S, \circ}$ can be referred to as the group of units of $\struct {S, \circ}$.
This can be denoted explicitly as $\struct {U_S, \circ}$.
Group of Units of Ring
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 $\struct {U_R, \circ}$.