integral closure IntegralClosure 2002-01-05 01:33:46 2002-06-09 19:30:54 Definition ring of integers \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $B$ be a ring with a subring $A$. The {\em integral closure} of $A$ in $B$ is the set $A' \subset B$ consisting of all elements of $B$ which are integral over $A$. It is a theorem that the integral closure of $A$ in $B$ is itself a ring. In the special case where $A = \mathbb{Z}$, the integral closure $A'$ of $\mathbb{Z}$ is often called the {\em ring of integers} in $B$.