Ring

Group of units

For any ring there exists a group of units or multiplicative group under ring multiplication, #m/def/ring containing all units. This is clearly a group since it contains the multiplicative identity, is associative, and every element has an inverse.

Properties

• For a division ring , the multiplicative group as a set
• Finite subgroup of the group of units of a field is cyclic

#state/tidy | #lang/en | #SemBr