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  3. problem 3. let f ? e be a field extension. (i) sup

Problem 3. Let F ? E be a field extension. (i) Suppose ? ? E is...

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Advance Math

Problem 3. Let F ? E be a field extension.

(i) Suppose ? ? E is algebraic of odd degree over F. Prove thatF(?) = F(?^2 ). Hints: look at the tower of extensions F ? F(?^2 )? F(?) and their degrees.

(ii) Let S be a (possibly infinite) subset of E. Assume thatevery element of S is algebraic over F. Prove that F(S) = F[S]

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