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

Sources

• 1978: John S. Rose: A Course on Group Theory ... (previous) ... (next): $2$: Examples of Groups and Homomorphisms: $2.3$