From 385db80750dce2b87fb49784814ee660123ca7ff Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Thu, 18 Mar 2021 13:21:18 +0100
Subject: =?UTF-8?q?slides=20=C3=BCber=20Ideale?=
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---
 vorlesungen/slides/3/nichthauptideal.tex | 78 ++++++++++++++++++++++++++++++++
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 create mode 100644 vorlesungen/slides/3/nichthauptideal.tex

(limited to 'vorlesungen/slides/3/nichthauptideal.tex')

diff --git a/vorlesungen/slides/3/nichthauptideal.tex b/vorlesungen/slides/3/nichthauptideal.tex
new file mode 100644
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+++ b/vorlesungen/slides/3/nichthauptideal.tex
@@ -0,0 +1,78 @@
+%
+% nichthauptideal.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\bgroup
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\begin{frame}[t]
+\setlength{\abovedisplayskip}{5pt}
+\setlength{\belowdisplayskip}{5pt}
+\frametitle{Nicht-Hauptideal in $\mathbb{Z}[X]$}
+\vspace{-20pt}
+\begin{columns}[t,onlytextwidth]
+\begin{column}{0.48\textwidth}
+\begin{block}{Hauptideal\uncover<2->{ = ``Gerade''}}
+\vspace{-10pt}
+\begin{align*}
+\langle X+1\rangle&=(X+1) = {\color{red}(X+1)\cdot\mathbb{Z}[X]}
+\end{align*}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=0.4]
+\draw[->] (-6.3,0) -- (6.8,0) coordinate[label={$\mathbb{Z}$}];
+\draw[->] (0,-6.2) -- (0,6.6) coordinate[label={right:$\mathbb{Z}X$}];
+\foreach \x in {-6,...,6}{
+	\fill[color=red] (\x,\x) circle[radius=0.12];
+}
+\end{tikzpicture}
+\end{center}
+\end{block}
+\end{column}
+\begin{column}{0.48\textwidth}
+\uncover<3->{%
+\begin{block}{Ideal mit zwei Erzeugenden}
+\vspace{-10pt}
+\begin{align*}
+\uncover<6->{
+{\color{darkgreen}
+\langle 2,X\rangle
+}
+&=}
+\uncover<5->{
+{\color{red}2\cdot\mathbb{Z}[X]}
+}
+\uncover<6->{+}
+\uncover<4->{
+{\color{blue}X\cdot\mathbb{Z}[X]}
+}
+\end{align*}
+\begin{center}
+\begin{tikzpicture}[>=latex,thick,scale=0.4]
+\draw[->] (-6.3,0) -- (6.9,0) coordinate[label={$\mathbb{Z}$}];
+\draw[->] (0,-6.2) -- (0,7.0) coordinate[label={right:$\mathbb{Z}X$}];
+\uncover<6->{
+	\foreach \x in {-6,-4,...,6}{
+		\foreach \y in {-6,...,6}{
+			\fill[color=darkgreen] (\x,\y) circle[radius=0.20];
+		}
+	}
+}
+\uncover<5->{
+	\foreach \x in {-6,-4,...,6}{
+		\foreach \y in {-6,-4,...,6}{
+			\fill[color=red] (\x,\y) circle[radius=0.16];
+		}
+	}
+}
+\uncover<4->{
+	\foreach \y in {-6,...,6}{
+		\fill[color=blue] (0,\y) circle[radius=0.12];
+	}
+}
+\end{tikzpicture}
+\end{center}
+\end{block}}
+\end{column}
+\end{columns}
+\end{frame}
+\egroup
-- 
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