Center of Division Ring is Subfield

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Theorem

Let $\struct {K, +, \circ}$ be an division ring.

Then $\map Z K$, the center of $K$, is a subfield of $K$.


Proof

For $\map Z K$ to be a subfield of $K$, it needs to be a division ring that is commutative.

Thus the result follows directly from Center of Ring is Commutative Subring.

$\blacksquare$


Sources