From 2204004e6397ae96967d98150bcf07101d646870 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= Date: Wed, 16 Feb 2022 01:32:03 +0100 Subject: [PATCH] fix tizkcd figure --- 2021_Algebra_I.tex | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/2021_Algebra_I.tex b/2021_Algebra_I.tex index dc0d785..f53507e 100644 --- a/2021_Algebra_I.tex +++ b/2021_Algebra_I.tex @@ -851,14 +851,12 @@ The following will lead to another proof of the Nullstellensatz, which uses the \label{artintate} Let $A$ be a subalgebra of the $R$-algebra $B$, where $R$ is Noetherian. If $ B / R$ is of finite type and $B / A$ is finite, then $A / R$ is also of finite type. - \begin{figure}[H] - \centering + \[ \begin{tikzcd} A \arrow[hookrightarrow]{rr}{\subseteq}& & B \\ &R \arrow{ul}{\alpha} \arrow{ur}{\alpha} \text{~(Noeth.)} \end{tikzcd} - \end{figure} - + \] \end{proposition} \begin{proof} Let $(b_i)_{i=1}^{m}$ generate $B$ as an $A$-module and $(\beta_j)_{j=1}^m$ as an $R$-algebra.