Question
Let $a$ and $b$ belong to some extension field of $F$ and let $b$ be algebraic over $F$. Prove that $[F(a, b): F(a)] \leq[F(a, b): F]$.
Step 1
We are given that $a$ and $b$ belong to some extension field $E$ of $F$, and that $b$ is algebraic over $F$. We want to show that $[F(a, b): F(a)] \leq [F(a, b): F]$. Show more…
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