Multiplicative Group of Field is Abelian Group/Proof 2

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Theorem

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.


Proof

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

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

$\blacksquare$


Sources