diff --git a/4. Semester/ALGZTH/TeX_files/Korper/Wurzelkorper_Zerfallungskorper.tex b/4. Semester/ALGZTH/TeX_files/Korper/Wurzelkorper_Zerfallungskorper.tex
index 8a4348f..9cc183c 100644
--- a/4. Semester/ALGZTH/TeX_files/Korper/Wurzelkorper_Zerfallungskorper.tex	
+++ b/4. Semester/ALGZTH/TeX_files/Korper/Wurzelkorper_Zerfallungskorper.tex	
@@ -105,11 +105,11 @@ Sei $K$ ein Körper, $f \in K[X]$ mit $n = \deg(f) > 0$.
 	\end{enumerate}
 \end{example}
 \begin{*example}
-	Sei $f = x^3 -2 \in \Q[X]$, dann sind die Nullstellen von $f$: $\sqrt[2]{3} \in \R, \zeta_3\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3}$
+	Sei $f = x^3 -2 \in \Q[X]$, dann sind die Nullstellen von $f$: $\sqrt[2]{2} \in \R, \zeta_3\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2}$
 	\begin{itemize}
-		\item $\Q(\sqrt[2]{3})$ ist Wurzelkörper von $f$. $\Q(\sqrt[2]{3}) \subseteq \R, \zeta_3\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3} \notin \R$, aber kein Zerfällungskörper. Der Zerfällungskörper von $f$ ist
+		\item $\Q(\sqrt[2]{2})$ ist Wurzelkörper von $f$. $\Q(\sqrt[2]{2}) \subseteq \R, \zeta_3\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2} \notin \R$, aber kein Zerfällungskörper. Der Zerfällungskörper von $f$ ist
 		\begin{align*}
-			\Q(\sqrt[2]{3},\zeta_3\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3}) = \Q(\sqrt[2]{3}, \zeta_3^2 \sqrt[2]{3})
+			\Q(\sqrt[2]{2},\zeta_3\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2}) = \Q(\sqrt[2]{2}, \zeta_3^2 \sqrt[2]{2})
 		\end{align*}
 	\end{itemize}
 \end{*example}
diff --git a/4. Semester/ALGZTH/Vorlesung ALGZTH.pdf b/4. Semester/ALGZTH/Vorlesung ALGZTH.pdf
index 2e6a912..c64df11 100644
Binary files a/4. Semester/ALGZTH/Vorlesung ALGZTH.pdf and b/4. Semester/ALGZTH/Vorlesung ALGZTH.pdf differ
diff --git a/Material/ALG/lemma_1_3_12.pdf b/Material/ALG/lemma_1_3_12.pdf
new file mode 100644
index 0000000..d170de4
Binary files /dev/null and b/Material/ALG/lemma_1_3_12.pdf differ
diff --git a/Material/ALG/lemma_1_3_12.tex b/Material/ALG/lemma_1_3_12.tex
new file mode 100644
index 0000000..f28617f
--- /dev/null
+++ b/Material/ALG/lemma_1_3_12.tex
@@ -0,0 +1,40 @@
+\documentclass{standalone}
+
+
+\usepackage{tikz, amsmath}
+%	\usepackage{tikz-qtree}
+	\usepackage{tikz-cd}
+%	\usetikzlibrary{cd}
+%	\usetikzlibrary{arrows}
+%	\usetikzlibrary{automata}
+%	\usetikzlibrary{babel}
+%	\usetikzlibrary{calc}
+%	\usetikzlibrary{fit}
+%	\usetikzlibrary{matrix}
+%	\usetikzlibrary{positioning}
+%	\usetikzlibrary{shapes.geometric}
+%	\usetikzlibrary{arrows.meta,bending}
+
+\begin{document}
+	\begin{align*}
+%		\begin{tikzcd}[ampersand replacement=\&]
+%			L \arrow[r, "\sigma"]   \& L' K \arrow[r, "\varphi"]
+%			\arrow[u] \& K' \arrow[u]
+%		\end{tikzcd}
+		\begin{tikzcd}[ampersand replacement=\&]
+			L \arrow[r, "\sigma"] \arrow[d] \& L' \arrow[d] \\
+			K \arrow[r, "\phi"] \& \tilde{K}
+		\end{tikzcd}\\
+		\begin{tikzcd}
+		A \arrow[r, "\phi"] \arrow[d, red]
+		\& B \arrow[d, "\psi" red] \\
+		C \arrow[r, red, "\eta" blue]
+		\& D
+		\end{tikzcd}
+	\end{align*}
+%	
+%	\begin{tikzcd}
+%	L \arrow[dd] \arrow[rr] \&         \& L' \arrow[dd] \\
+%	K \arrow[rr]            \&         \& K'           
+%	\end{tikzcd}
+\end{document}
diff --git a/cwl/mathscript - Copy.cwl b/cwl/mathscript - Copy.cwl
new file mode 100644
index 0000000..f893020
--- /dev/null
+++ b/cwl/mathscript - Copy.cwl	
@@ -0,0 +1,98 @@
+#include:tabularx
+#include:longtable
+#include:multirow
+#include:colortbl
+#include:amsmath
+#include:amssymb
+#include:amsfonts
+#include:mathtools
+#include:latexsym
+#include:marvosym
+#include:stdmaryd
+#include:bbm
+#include:wasysym
+#include:mathafla
+#include:cancel
+#include:xfrac
+#include:xcolor
+#include:graphicx
+#include:tcolorbox
+#include:pgfplots
+#include:pgf
+#include:tikz
+#include:ulem
+#include:marginnote
+#include:enumerate
+#include:enumitem
+#include:listings
+#include:hyperref
+#include:cleveref
+#include:bookmark
+#include:ntheorem
+#include:mathoperators
+\begin{theorem}
+\begin{theorem}[title]
+\end{theorem}
+\begin{proposition}
+\begin{proposition}[title]
+\end{proposition}
+\begin{lemma}
+\begin{lemma}[title]
+\end{lemma}
+\begin{definition}
+\begin{definition}[title]
+\end{definition}
+\begin{conclusion}
+\begin{conclusion}[title]
+\end{conclusion}
+\begin{remark}
+\begin{remark}[title]
+\end{remark}
+\begin{erinnerung}
+\begin{erinnerung}[title]
+\end{erinnerung}
+\begin{example}
+\begin{example}[title]
+\end{example}
+\begin{algorithm}
+\begin{algorithm}[title]
+\end{algorithm}
+\begin{*definition}
+\begin{*definition}[title]
+\end{*definition}
+\begin{*remark}
+\begin{*remark}[title]
+\end{*remark}
+\begin{*example}
+\begin{*example}[title]
+\end{*example}
+\begin{*anmerkung}
+\begin{*anmerkung}[title]
+\end{*anmerkung}
+\begin{mathematica}
+\begin{mathematica}[title]
+\end{mathematica}
+\begin{overview}
+\begin{overview}[title]
+\end{overview}
+\begin{interpretation}[title]
+\end{interpretation}
+\begin{underlinedPlain}[title]
+\end{underlinedPlain}
+\begin{hint}
+\end{hint}
+\begin{plainenvironment}[title]
+\end{plainenvironment}
+\begin{underlinedenvironment}[title]
+\end{underlinedenvironment}
+\begin{boldEnvironment}[title]
+\end{boldEnvironment}
+\begin{repetition}
+\end{repetition}
+\begin{proof}
+\begin{proof}[title]
+\end{proof}
+\proplbl{label}#l
+\propref{ref}#r
+\begriff{term}%text
+\begriff[Ordnung]{term}[Unterordnung]%text