Multiplicative Group of Field is Abelian Group/Proof 2

From ProofWiki
Jump to navigation Jump to search


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

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

The algebraic structure $\struct {F^*, \times}$ is an abelian group.


Recall that a field is a non-trivial commutative division ring.

The result follows from Non-Zero Elements of Division Ring form Group.