Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings, (II)
Abstract
Let 1 < s1 < . . . < sk be integers, and assume that κ ≥ 2 (so sk ≤ 3). Then there exists a local UFD (Unique Factorization Domain) (R,M) such that:
(1) Height(M) = sk.
(2) R = R' = ∩{VI (V,N) € Vj}, where Vj (j = 1, . . . , κ) is the set of all of the Rees valuation rings (V,N) of the M-primary ideals such that trd((V I N) I (R I M)) = sj - 1.
(3) With V1, . . . , Vk as in (2), V1 ∪ . . . Vk is a disjoint union of all of the Rees valuation rings of allof the M-primary ideals, and each M-primary ideal has at least one Rees valuation ring in each Vj.
Department(s)
Mathematics
Document Type
Article
DOI
https://doi.org/10.18311/jims/2017/6133
Keywords
integral closure, local domain, Rees Valuation Ring, unique factorization domain
Publication Date
2017
Recommended Citation
Kemp, Paula, Louis J. Ratliff, and Kishor Shah. "Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings (II)." The Journal of the Indian Mathematical Society 84, no. 1-2 (2017).
Journal Title
The Journal of the Indian Mathematical Society
