JOURNAL OF ALGEBRA | 卷:323 |
Bases of ideals and Rees valuation rings | |
Article | |
Heinzer, William J.1  Ratliff, Louis J., Jr.2  Rush, David E.2  | |
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA | |
[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA | |
关键词: Rees valuations; Rees good basis; Projectively equivalent ideals; Asymptotic prime divisors; Asymptotic sequence; Unramified extension; | |
DOI : 10.1016/j.jalgebra.2009.07.026 | |
来源: Elsevier | |
【 摘 要 】
Let I be a regular proper ideal in a Noetherian ring R. We prove that there exists a simple free integral extension ring A of R such that the ideal IA has a Rees-good basis; that is, a basis c(1),...,c(g) such that c(i)W = IW for i = 1,...,g and for all Rees valuation rings W of IA. Moreover, A may be constructed so that: (i) IA and I have the same Rees integers (with possibly different cardinalities), and (ii) A(P) is unramified over R(P boolean AND R) for each asymptotic prime divisor P of IA. Indeed, if H is a regular ideal in R such that each asymptotic prime divisor of H is contained in an asymptotic prime divisor of I, then (ii) holds for HA. If Card(Rees H) <= Card(Rees I), we prove that (i) also holds for HA and H. If I = (b1,...,b(g))R and b1,...,b(g) is an asymptotic sequence. we prove that b(1),...,b(g) is a Rees-good basis of I. (C) 2009 Elsevier Inc. All rights reserved.
【 授权许可】
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