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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?

Thanks.

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    No problem. I'll post an answer to prevent Community bumps.2011-12-04

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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.