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13A15-EntriesOnFinitelyGeneratedIdeals.tex
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13A15-EntriesOnFinitelyGeneratedIdeals.tex
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\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{EntriesOnFinitelyGeneratedIdeals}
\pmcreated{2015-05-06 15:39:55}
\pmmodified{2015-05-06 15:39:55}
\pmowner{pahio}{2872}
\pmmodifier{pahio}{2872}
\pmtitle{entries on finitely generated ideals}
\pmrecord{17}{37244}
\pmprivacy{1}
\pmauthor{pahio}{2872}
\pmtype{Topic}
\pmcomment{trigger rebuild}
\pmclassification{msc}{13A15}
\pmclassification{msc}{13C05}
\pmclassification{msc}{16D25}
%\pmkeywords{commutative ring}
%\pmkeywords{finitely generated}
%\pmkeywords{finitely generated ideal}
\pmrelated{ProductOfFinitelyGeneratedIdeals}
\pmrelated{TopicsOnIdeals}
\endmetadata
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
\usepackage{amsthm}
% making logically defined graphics
%%%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here
\theoremstyle{definition}
\newtheorem*{thmplain}{Theorem}
\begin{document}
This entry lists PlanetMath entries concerning finitely generated ideals of commutative rings.
\textbf{One \PMlinkescapetext{generator}}
\begin{enumerate}
\item principal ideal
\item zero ideal
\item unit ideal
\item principal ideal ring
\item principal ideal domain
\item B\'ezout ring
\item divisibility by product
\end{enumerate}
\textbf{Two \PMlinkescapetext{generators}}
\begin{enumerate}
\item two-generator property
\item multiplication rule gives inverse ideal
\item invertibility of regularly generated ideal
\item unique factorization and ideals in ring of integers
\end{enumerate}
\textbf{{\em n} \PMlinkescapetext{generators}}
\begin{enumerate}
\item invertible ideal is finitely generated
\item generators of inverse ideal
\item \PMlinkname{invertibility of regularly generated ideal}{InvertibilityOfRegularlyGeneratedIdeal}
\item \PMlinkname{Pr\"ufer ring}{pruferring}
\item \PMlinkname{Pr\"ufer domain}{pruferdomain}
\item ideal generators in Pr\"ufer ring
\item finitely generated modules over a principal ideal domain
\end{enumerate}
\textbf{Formulae}
\begin{enumerate}
\item well-definedness of product of finitely generated ideals
\item product of finitely generated ideals
\item cancellation ideal
\item ideal decomposition in Dedekind domain
\item ideal inverting in Pr\"ufer ring
\item least common multiple
\item quotient of ideals
\item generators of a quotient polynomial ring
\end{enumerate}
%%%%%
%%%%%
\end{document}