Wedderburn's Theorem

Theorem
Every finite division ring $$D$$ is a field.

Proof
Let D be a finite division ring. If D is shown commutative then D is a field. Denote $$Z(D) = \{z \in D|zd = dz \forall d \in D \}$$ called the center of the ring. Then

He first published it in 1905. However, his proof had a gap in it.

The first complete proof was supplied by Leonard Dickson.

It is also known as Wedderburn's Little Theorem.