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

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Authors

  • ,US
  • ,US
  • ,US

DOI:

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

Keywords:

Integral Closure, Noetherian Domain, Local Domain, Rees Valuation Ring
Geometry

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.

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Published

2017-01-02

How to Cite

Kemp, P., Ratliff, Jr., L. J., & Shah, K. (2017). Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings, (I). The Journal of the Indian Mathematical Society, 84(1-2), 43–54. https://doi.org/10.18311/jims/2017/6108
Received 2016-06-09
Accepted 2016-06-14
Published 2017-01-02

 

References

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