Article ID Journal Published Year Pages File Type
4585200 Journal of Algebra 2013 13 Pages PDF
Abstract

We study the question of obtaining uniform bounds for the growth of symbolic powers of ideals in Noetherian rings. First we use a generalized version of Artinʼs strong approximation theorem to obtain uniform bounds for prime ideals in the integral closure of a finite Galois field extension of the fraction field of an excellent Henselian regular local ring. As a corollary, we obtain a similar result for a complete Noetherian local domains. We also obtain linear uniform bounds for the growth of symbolic powers in certain normal subrings of equicharacteristic regular rings under mild conditions.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory