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2748 solutionsIf is prime and is algebraic over , show that either or .
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If and is algebraic over , prove that is algebraic over .
State and prove the Euclidean algorithm for finding the gcd of two elements of a Euclidean domain.
Prove that every ideal in is finitely generated (Theorem 6.3) as follows. Let and let { for some }.
If V is a nonzero element of V, prove that is linearly independent over F.
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