integral closure

Let B be a ring with a subring A. The integral closureMathworldPlanetmath of A in B is the set AB 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=, the integral closure A of 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