integral closure

Let $B$ be a ring with a subring $A$. The integral closure of $A$ in $B$ is the set $A^{\prime }\subset B$ 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 $A^{\prime }$ of $\mathbb{Z}$ is often called the ring of integers in $B$.

Title	integral closure
Canonical name	IntegralClosure
Date of creation	2013-03-22 12:07:53
Last modified on	2013-03-22 12:07:53
Owner	djao (24)
Last modified by	djao (24)
Numerical id	8
Author	djao (24)
Entry type	Definition
Classification	msc 13B22
Related topic	IntegrallyClosed
Defines	ring of integers