From 34830c70eff17735318b34e588307bd83ae49a27 Mon Sep 17 00:00:00 2001 From: Aise Johan de Jong Date: Mon, 16 Jan 2023 15:03:42 -0500 Subject: [PATCH] bigcup -> bigoplus THanks to Ben Moonen https://stacks.math.columbia.edu/tag/08XV#comment-7771 --- dualizing.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/dualizing.tex b/dualizing.tex index e0bf253c1..c854834d8 100644 --- a/dualizing.tex +++ b/dualizing.tex @@ -296,13 +296,13 @@ \section{Injective modules} \begin{proof} Let $E_i$ be a family of injective modules parametrized by a set $I$. -Set $E = \bigcup E_i$. To show that $E$ is injective we use +Set $E = \bigoplus E_i$. To show that $E$ is injective we use Injectives, Lemma \ref{injectives-lemma-criterion-baer}. Thus let $\varphi : I \to E$ be a module map from an ideal of $R$ into $E$. As $I$ is a finite $R$-module (because $R$ is Noetherian) we can find finitely many elements $i_1, \ldots, i_r \in I$ -such that $\varphi$ maps into $\bigcup_{j = 1, \ldots, r} E_{i_j}$. -Then we can extend $\varphi$ into $\bigcup_{j = 1, \ldots, r} E_{i_j}$ +such that $\varphi$ maps into $\bigoplus_{j = 1, \ldots, r} E_{i_j}$. +Then we can extend $\varphi$ into $\bigoplus_{j = 1, \ldots, r} E_{i_j}$ using the injectivity of the modules $E_{i_j}$. \end{proof}