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Algebraic extension
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== Relative algebraic closures == Given a field ''k'' and a field ''K'' containing ''k'', one defines the '''relative algebraic closure''' of ''k'' in ''K'' to be the subfield of ''K'' consisting of all elements of ''K'' that are algebraic over ''k'', that is all elements of ''K'' that are a root of some nonzero polynomial with coefficients in ''k''.
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