If K is contained in R contained in F and F is algebraic over K, show R is a field

morphism

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.

morphism Recognitions: Homework Help Science Advisor	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.