from old to new

Author: dirichy

.gitattributes

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+AlgebraicGeometry

.gitignore

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+1

.vscode/settings.json

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+%! Mode:: "TeX:UTF-8"
+%!TEX encoding = UTF-8 Unicode
+%!TEX TS-program = xelatex
+\documentclass{ctexart}
+\usepackage{bbm}
+\usepackage{tikz}
+\usepackage{amsmath,amssymb,amsthm,color,mathrsfs}
+\usepackage{hyperref}
+\usepackage{cleveref}
+\usepackage{enumitem,anysize}%
+\usepackage{expl3}
+\marginsize{1in}{1in}{1in}{1in}%
+\theoremstyle{remark}
+\newtheorem*{claim*}{Claim}
+\newtheorem{lemma}{Lemma}
+
+\DeclareMathOperator{\ot}{ordertype}
+\DeclareMathOperator{\dom}{dom}
+\DeclareMathOperator{\ran}{ran}
+\DeclareMathOperator{\field}{field}
+\DeclareMathOperator{\Ord}{Ord}
+
+\newcommand{\cc}{\mathfrak{c}}
+
+\def\email#1{{\texttt{#1}}}
+\newcommand{\isep}[1][0pt]{\addtolength{\itemsep}{#1}}
+\newcounter{problem}
+\renewcommand{\theproblem}{\Roman{problem}}
+\newenvironment{problem}{\refstepcounter{problem}\noindent\color{blue}\begin{tikzpicture}[baseline]%
+\node at (-0.02em,0.3em) {$\mathbb{P}$};%
+\node[scale=0.7] at (0.2em,-0.0em) {R};%
+\node[scale=0.7] at (0.6em,0.4em) {O};%
+\node[scale=0.8] at (1.05em,0.25em) {B};%
+\node at (1.55em,0.3em) {L};%
+\node[scale=0.7] at (1.75em,0.45em) {E};%
+\node at (2.35em,0.3em) {M};%
+\end{tikzpicture}\theproblem}{}
+\crefname{problem}{Problem}{Problem}
+%\renewcommand\theprob{{\Roman{problem}}}
+\newcommand\mysolution{\begin{tikzpicture}[baseline]%
+\node at (-0.04em,0.3em) {$\mathbb{S}$};%
+\node[scale=0.7] at (0.35em,0.4em) {O};%
+\node at (0.7em,0.3em) {\textit{L}};%
+\node[scale=0.7] at (0.95em,0.4em) {U};%
+\node[scale=1.1] at (1.19em,0.32em){T};%
+\node[scale=0.85] at (1.4em,0.24em){I};%
+\node at (1.9em,0.32em){$\mathcal{O}$};%
+\node[scale=0.75] at (2.3em,0.21em){\texttt{N}};%
+\end{tikzpicture}}
+\newenvironment{solution}{\begin{proof}[\mysolution]}{\end{proof}}
+
+%%%%%%%%
+\newcommand{\calL}{\mathcal{L}}
+
+\newcommand\<{\langle}
+\renewcommand\>{\rangle}
+\newcommand\eneg{\mathcal{E}_{\neg}}
+\newcommand\eto{\mathcal{E}_{\to}}
+\newcommand\N{\mathbb{N}}
+\newcommand\subini{\subsetneqq_{init}}
+\def\to{\rightarrow}
+\newcommand{\calA}{\mathcal{A}}
+\newcommand{\xor}{\vee}
+\newcommand{\bor}{\bigvee}
+\newcommand{\band}{\bigwedge}
+\newcommand{\xand}{\wedge}
+\newcommand{\minus}{\mathbin{\backslash}}
+\newcommand{\calF}{\mathcal{F}}
+\newcommand\mi[1]{\mathscr{P}(#1)}
+\newcommand{\calB}{\mathcal{B}}
+\newcommand{\heq}{\mathop{\hat{=}}}
+\newcommand{\hneq}{\mathop{\hat{\neq}}}
+\newcommand{\calR}{\mathcal{R}}
+\newcommand{\hle}{\mathop{\hat{<}}}
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\calM}{\mathcal{M}}
+\newcommand{\calN}{\mathcal{N}}
+\newcommand{\frA}{\mathfrak{A}}
+\newcommand{\card}{\mathrm{card}}
+\newcommand{\frM}{\mathfrak{M}}
+\newcommand{\Th}{\mathrm{Th}}
+\newcommand{\ecd}{\mathrm{EC}_\Delta}
+\newcommand{\Q}{\mathbb{Q}}
+\newcommand{\Z}{\mathbb{Z}}
+\newcommand{\oto}{\leftrightarrow}
+\newcommand{\hin}{\hat{\in}}
+\newcommand{\fun}[2]{{}^{#1}#2}
+\newcommand{\A}{\mathbbm{A}}
+
+
+
+
+
+
+
+
+\begin{document}
+\title{$\mathbb{ALGEBRAIC\ GEOMETRY}$}
+\author{白永乐\\ %% 姓名
+SID: 202011150087\\ %% 学号
+\email{[email protected]}} %% 电邮
+\maketitle
+\begin{problem}
+$P$ is an ideal of a unitary commutative ring $A$, then $P$ is prime ideal of $A\iff A/P$ is integral domain.
+\end{problem}
+
+\begin{problem}
+$M$ is an ideal of a unitary commutative ring $A$, then $M$ is maximal ideal of $A \iff A/M$ is a field.   
+\end{problem}
+
+\begin{problem}
+A ring $A$ is noetherian, $I\subset A$ is an ideal of $A$, then $A/I$ is noetherian. 
+\end{problem}
+
+\begin{problem}
+\label{pro:4}
+$K$ is a field, $A=K[x_1,x_2,\cdots x_n],\A^n_K=K^n$. For ideal $I$ of $A$ let $V(I):=\{p\in\A_K^n:f(p)=0,\forall f\in I\}$. Then $V(I_1)\cup V(I_2)=V(I_1\cap I_2)=V(I_1I_2)$
+\end{problem}
+
+\begin{problem}
+$K$ is an infinite field, then $\A_k^n$ is not Hausdorff. 
+\end{problem}
+
+\end{document}

AlgebraicGeometry/.subject

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+2