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I have a question:

Let $F$ be an extension field over $K$.

Let $u\in F$. Show that $u$ is algebraic over $K$ $\iff$ the subspace spanned by $\{1,u,u^2,\ldots, u^n\}$ is a field.

I have problems with the $\Leftarrow$ part.

Vinyl_cape_jawa
  • 4,794
  • Question is incomplete... what subspace are you referring to when you say "subspace spanned by ${1,u,u^2,…,u^n}$ then $u$ is algebraic over $K$." –  May 20 '14 at 11:00
  • Possible duplicate of http://math.stackexchange.com/questions/397733/algebraic-field-extension-question. My answer there answers this question. – lhf May 20 '14 at 11:34

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$u$ has an inverse: then obtain a relation.