10 lines
497 B
TeX
10 lines
497 B
TeX
\section{The Fundamental Theorem of Field Theory}
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\begin{definition}[Extension Field]
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A field $\E$ is an \textit{extension field} of a field $\F$ if $\F \subseteq \E$ and the operations of $\F$ are those of $\E$ restricted to $\F$.
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\end{definition}
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\begin{theorem}[Fundamental Theorem of Field Theory (Kronecker's Theorem, 1887)]
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Let $\F$ be a field and let $f(x)$ be a nonconstant polynomial in $\F[x]$. Then there is an extension field $\E$ of $\F$ in which $f(x)$ has a zero.
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\end{theorem}
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