Definition:Multiplicative Group

Definition

Let $\struct {F, +, \times}$ be a field.

Let $F^* := F \setminus \set 0$ be the set $F$ less its zero.

The group $\struct {F^*, \times}$ is known as the multiplicative group of $F$.

Also see

• Multiplicative Group of Field is Abelian Group: by definition of a field, the multiplicative group of a field is abelian.

Sources

• 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 2$. Elementary Properties