Specialization and Integral Closure
Commutative Algebra
2014-04-08 v3
Abstract
We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional assumptions, we show that an element is integral over a module if it is integral modulo a generic element of the module. This turns questions about integral closures of modules into problems about integral closures of ideals, by means of a construction known as Bourbaki ideal.
Keywords
Cite
@article{arxiv.math/0611773,
title = {Specialization and Integral Closure},
author = {J. Hong and B. Ulrich},
journal= {arXiv preprint arXiv:math/0611773},
year = {2014}
}