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Fix typo in galois.tex (vEnhance#159)
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* Update galois.tex

Fix typo:  "The splitting field of F" should be "The splitting field of p(x)"

* Update galois.tex

Complete the previous fix...
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su1yu4n authored Oct 9, 2022
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2 changes: 1 addition & 1 deletion tex/alg-NT/galois.tex
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Expand Up @@ -392,7 +392,7 @@ \section{Automorphism groups and Galois extensions}
\begin{definition}
Let $F$ be a field and $p(x) \in F[x]$ a polynomial of degree $n$.
Then $p(x)$ has roots $\alpha_1, \dots, \alpha_n$ in an algebraic closure of $F$.
The \vocab{splitting field} of $F$ is defined as $F(\alpha_1, \dots, \alpha_n)$.
The \vocab{splitting field} of $p(x)$ over $F$ is defined as $F(\alpha_1, \dots, \alpha_n)$.
\end{definition}
In other words, the splitting field is the smallest field in which $p(x)$ splits.
\begin{example}[Examples of splitting fields]
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