Show that $b$ is algebraic over $K(a)$, the subfield of $L$ generated by $K$ and $a$, if and only if $a$ is algebraic over $K(b)$.
Let $a, b\in L\supset K$ be transcendental over $K$.
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abstract-algebra
ring-theory
1 Answers
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Hint: Both statements say that there is a 2 variable polynomial $f\in K[x,y]$ such that $f(a,b)=0$.