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Maximilian Keßler 2022-02-16 01:21:07 +01:00
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2021_Algebra_I.tex
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@ -31,7 +31,7 @@ Fields which are not assumed to be algebraically closed have been renamed (usual
\pagebreak \pagebreak
\subseteqction{Finiteness conditions} \subsection{Finiteness conditions}
\subsection{Finitely generated and Noetherian modules} \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 $b_i$. This contradicts the minimality of $n$, as $B$ can be generated by $< n$ elements $b_i$.
\end{proof} \end{proof}
\subseteqction{The Nullstellensatz and the Zariski topology} \subsection{The Nullstellensatz and the Zariski topology}
\subsection{The Nullstellensatz} %LECTURE 1 \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. 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 % Lecture 11
\subseteqction{Projective spaces} \subsection{Projective spaces}
Let $\mathfrak{l}$ be any field. Let $\mathfrak{l}$ be any field.
\begin{definition} \begin{definition}
For a $\mathfrak{l}$-vector space $V$, let $\bP(V)$ be the set of one-dimensional subspaces of $V$. 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 % Lecture 13
\subseteqction{Varieties} \subsection{Varieties}
\subsection{Sheaves} \subsection{Sheaves}
@ -2934,7 +2934,7 @@ Original (Noether normalization)
Artin-Tate Artin-Tate
Uncountable fields Uncountable fields
\begin{landscape} \begin{landscape}
\subseteqction{Übersicht} \subsection{Übersicht}
{\rowcolors{2}{gray!10}{white} {\rowcolors{2}{gray!10}{white}
\begin{longtable}{lll} \begin{longtable}{lll}
\end{longtable} \end{longtable}