Projective equivalence of ideals in Noetherian integral domains
Commutative Algebra
2007-12-07 v1
Abstract
Let I be a nonzero proper ideal in a Noetherian integral domain R. In this paper we establish the existence of a finite separable integral extension domain A of R and a positive integer m such that all the Rees integers of IA are equal to m. Moreover, if R has altitude one, then all the Rees integers of J = Rad(IA) are equal to one and the ideals J^m and IA have the same integral closure. Thus Rad(IA) = J is a projectively full radical ideal that is projectively equivalent to IA. In particular, if R is Dedekind, then there exists a Dedekind domain A having the following properties: (i) A is a finite separable integral extension of R; and (ii) there exists a radical ideal J of A and a positive integer m such that IA = J^m.
Keywords
Cite
@article{arxiv.0712.0833,
title = {Projective equivalence of ideals in Noetherian integral domains},
author = {William J. Heinzer and Louis J. Ratliff and David E. Rush},
journal= {arXiv preprint arXiv:0712.0833},
year = {2007}
}
Comments
20 pages