Definition:Multiplicative Group
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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