Let $D$ be a division ring. Show that if every $a \in D$ is algebraic over the prime subfield of $D$ then $D$ is commutative ($D=Z(D)$).
closed as off-topic by Xam, Stefan4024, quid♦ Nov 25 '17 at 21:53
This question appears to be off-topic. The users who voted to close gave this specific reason:
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A counterexample is $\mathbb Q(i,j,k)$ inside the quaternions. (Use that every pure quaternion has a real square.)