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Corollary 26, p. 232 in Lang starts as follows.

"Let $E$ be an extension of the field $k$ which is algebraically closed and let $k^a$ be the union of all sub extensions of $E$, which are algebraic over $k$."

My question is: why is $k^a$ non-empty?


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Right! Thanks a lot. If you want write this as an answer and i'll accept it. – Manos Dec 4 '11 at 18:34
No problem. I'll post an answer to prevent Community bumps. – Dylan Moreland Dec 4 '11 at 19:05
up vote 0 down vote accepted

There's always one subextension of $E/k$ which is algebraic over $k$, namely $k$. But there will be others unless $k$ is already algebraically closed.

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