Definition:Group of Units/Monoid

Definition
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 $\struct {U_S, \circ}$.

Also see

 * Invertible Elements of Monoid form Subgroup


 * Definition:Group of Units of Ring