Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings, (I)
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.
integral closure, noetherian domain, local domain, rees valuation ring
Kemp, Paula, Louis J. Ratliff, and Kishor Shah. "Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings (I)." The Journal of the Indian Mathematical Society 84, no. 1-2 (2017).
The Journal of the Indian Mathematical Society