If K is contained in R contained in F and F is algebraic over K, show R is a field
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Feb19-12, 09:31 PM
Let a be a nonzero element of R. Here are two independent (but ultimately equivalent) hints to help you show that the inverse of a belongs to R.
Hint A: K(a)=K[a].
Hint B: Write down the inverse of a in F, using the fact that a is algebraic/K.