irreducible Irreducible 2001-11-04 21:34:38 2005-05-01 14:08:34 Definition irreducible element \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $r$ be a non-unit of an integral domain $D$. \,We say that $r$ is \emph{irreducible} in $D$, if any factorization \,$r = ab$\, in $D$ requires that $a$ or $b$ is a unit.