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arXiv · 0712.0833

Projective equivalence of ideals in Noetherian integral domains

William J. Heinzer·Louis J. Ratliff Jr·David E. Rush
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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.

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William J. Heinzer, Louis J. Ratliff Jr, David E. Rush. 2007-12-05. Projective equivalence of ideals in Noetherian integral domains. https://arxiv.org/abs/0712.0833

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