10 lines
454 B
TeX
10 lines
454 B
TeX
\section{Properties of Algebraic Extensions}
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\begin{theorem}[Algebraic over Algebraic Is Algebraic]
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If $\K$ is an algebraic extension of $\E$ and $\E$ is an algebraic extension of $\F$, then $\K$ is an algebraic extension of $\F$.
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\end{theorem}
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\begin{corollary}[Subfield of Algebraic Elements]
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Let $\E$ be an extension field of the field $\F$. Then the set of all elements of $\E$ that are algebraic over $\F$ is a subfield of $\E$.
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\end{corollary}
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