DenseIdealssubsetsOfARing 2006-10-29 12:57:33 2009-03-30 17:50:32 Definition dense subset of a ring dense subset right dense left dense % 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 Given a commutative ring $R$, an ideal/subset $I\subset R$ is said to be \PMlinkescapetext{\emph{dense}} iff its annihilator is $\{0\}$, in other words $$\mathrm{Ann}(I)=\{0\}$$ We can similarly define \PMlinkescapetext{\emph{right dense}} and \PMlinkescapetext{\emph{left dense}} in the case of noncommutative rings.