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typo (the index "j" was already used for the "y_j")

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iblech authored and aisejohan committed May 21, 2017
1 parent 505b9b5 commit 9d71d07ad96f1a1a108f1cee1e0d1cba01e724f9
Showing with 2 additions and 2 deletions.
  1. +2 −2 algebra.tex
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@@ -564,12 +564,12 @@ \section{Ring maps of finite type and of finite presentation}
\begin{proof}
Write $S = R[y_1, \ldots, y_m]/(f_1, \ldots, f_k)$.
Choose $g_i \in R[y_1, \ldots, y_m]$ which are lifts
of $\alpha(x_i)$. Then we see that $S = R[x_i, y_j]/(f_j, x_i - g_i)$.
of $\alpha(x_i)$. Then we see that $S = R[x_i, y_j]/(f_l, x_i - g_i)$.
Choose $h_j \in R[x_1, \ldots, x_n]$ such that $\alpha(h_j)$
corresponds to $y_j \bmod (f_1, \ldots, f_k)$. Consider
the map $\psi : R[x_i, y_j] \to R[x_i]$, $x_i \mapsto x_i$,
$y_j \mapsto h_j$. Then the kernel of $\alpha$
is the image of $(f_j, x_i - g_i)$ under $\psi$ and we win.
is the image of $(f_l, x_i - g_i)$ under $\psi$ and we win.
\end{proof}
\begin{lemma}

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