Definition 9.26.9. Let $K/k$ be a field extension.

The

*algebraic closure of $k$ in $K$*is the subfield $k'$ of $K$ consisting of elements of $K$ which are algebraic over $k$.We say $k$ is

*algebraically closed in $K$*if every element of $K$ which is algebraic over $k$ is contained in $k$.

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