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

Authors

Paula Kemp, Missouri State UniversityFollow
Louis J. Ratliff
Kishor Shah, Missouri State UniversityFollow

Abstract

Let 1 < s1 < . . . < s_k be integers, and assume that κ ≥ 2 (so s_k ≤ 3). Then there exists a local UFD (Unique Factorization Domain) (R,M) such that:
(1) Height(M) = s_k.
(2) R = R' = ∩{VI (V,N) € V_j}, where V_j (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)) = s_j - 1.
(3) With V₁, . . . , V_k as in (2), V₁ ∪ . . . V_k 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 V_j.

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