Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings, (I)

Abstract

It is shown that the integral closure R' of a local (Noetherian) domain R is equal to the intersection of the Rees valuation rings of all proper ideals in R of the form (b, Ik)R, where b is an arbitrary nonzero nonunit in R and the Ik are an arbitrary descending sequence of ideals (varying with b and with Ik ⊆ (Ik-1 ∩ I1k) for all k > 1, one sequence for each b). Also, this continues to hold when b is restricted to being irreducible and no two distinct b are associates. We prove similar results for a Noetherian domain.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.18311/jims/2017/6108

Keywords

integral closure, noetherian domain, local domain, rees valuation ring

Publication Date

2017

Journal Title

The Journal of the Indian Mathematical Society

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