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

Abstract

Let 1 < s 1 < . . . < 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 V 1 , . . . , V κ as in (2), V 1 ∪ . . . V κ 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 .