Let B be a ring with a subring A. We will assume that A is contained in the center of B (in particular, A is commutativePlanetmathPlanetmathPlanetmath). An element xB is integral over A if there exist elements a0,,an-1A such that


The ring B is integral over A if every element of B is integral over A.

Title integral
Canonical name Integral
Date of creation 2013-03-22 12:07:44
Last modified on 2013-03-22 12:07:44
Owner djao (24)
Last modified by djao (24)
Numerical id 9
Author djao (24)
Entry type Definition
Classification msc 13B21
Related topic IntegralBasis