From 2366deba0adee5cb126d04cd872bc9f64f100bac Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Maximilian=20Ke=C3=9Fler?= <git@maximilian-kessler.de>
Date: Wed, 16 Feb 2022 01:21:07 +0100
Subject: [PATCH] fix subsection

---
 2021_Algebra_I.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/2021_Algebra_I.tex b/2021_Algebra_I.tex
index 96d32a1..64c5114 100644
--- a/2021_Algebra_I.tex
+++ b/2021_Algebra_I.tex
@@ -31,7 +31,7 @@ Fields which are not assumed to be algebraically closed have been renamed (usual
 \pagebreak
 
 
-\subseteqction{Finiteness conditions}
+\subsection{Finiteness conditions}
 
 \subsection{Finitely generated and Noetherian modules}
 
@@ -313,7 +313,7 @@ is injective. $n$ and the $a_i$ can be chosen such that $A$ is finite over the i
     This contradicts the minimality of $n$, as $B$ can be generated by $< n$ elements $b_i$.
 
 \end{proof}
-\subseteqction{The Nullstellensatz and the Zariski topology}
+\subsection{The Nullstellensatz and the Zariski topology}
 \subsection{The Nullstellensatz} %LECTURE 1
 Let $\mathfrak{k}$ be a field, $R \coloneqq \mathfrak{k}[X_1,\ldots,X_n], I \subseteq R$ an ideal.
 
@@ -1919,7 +1919,7 @@ $\rad(A) = f A$ where $f = \prod_{i=1}^{n} p_i$.
 
 % Lecture 11
 
-\subseteqction{Projective spaces}
+\subsection{Projective spaces}
 Let $\mathfrak{l}$ be any field.
 \begin{definition}
     For a $\mathfrak{l}$-vector space $V$, let $\bP(V)$ be the set of one-dimensional subspaces of $V$.
@@ -2284,7 +2284,7 @@ If $P_e $ with $e < d$ was $\neq 0$, it could not be a multiple of $P$ contradic
 
 
 % Lecture 13
-\subseteqction{Varieties}
+\subsection{Varieties}
 
 \subsection{Sheaves}
 
@@ -2934,7 +2934,7 @@ Original (Noether normalization)
 Artin-Tate
 Uncountable fields
 \begin{landscape}
-\subseteqction{Übersicht}
+\subsection{Übersicht}
 {\rowcolors{2}{gray!10}{white}
     \begin{longtable}{lll}
   \end{longtable}