band Band2 2002-08-19 19:15:23 2007-10-12 12:56:03 Definition idempotent % 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 A \emph{band} is a semigroup in which every element is idempotent. In semigroup theory, a commutative band is called a \emph{semilattice}. This is \PMlinkid{equivalent to the defintion of a semilattice}{3320} from the theory of partially ordered sets.