Parametric Decomposition of Monomial Ideals, II
Parametric Decomposition of Monomial Ideals, II
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单项式理想的参数分解，II
DOI：
10.1006/jabr.1997.6831
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发表时间：
1997
影响因子：
0.9
通讯作者：
Kishor Shah
中科院分区：
文献类型：
--
作者：
W. Heinzer;Ahmad Mirbagheri;L. Ratliff;Kishor Shah
摘要：设x 1，…，x d是交换环R中的R -序列，设I是单项式概念（因此I是由x 1 e 1···x de d的元素生成的，其中每个e I都是一个非负整数）。本文的主要成果有：(a)建立了当Rad(I) = Rad（(x 1，…，x d) R）时I的单根长度的实用计算公式；(b)确定有限多个单项式理想的交集再次成为单项式理想的充分必要条件；(c)表明,如果c R中的所有单项理想的集合包含我,关闭在有限的十字路口,那么每个理想J c有独特的分解作为irredundant有限交集的理想的形式(xτ(1)1,…,xτ(h) h) R,τ是{1,…,d}排列,h∈}{1,…,d, 1,…,h是正整数;(d)给出了R的某些形式环和Rees环的有关唯一参数分解定理的附加结果。
Abstract Let x 1 ,…, x d be an R -sequence in a commutative ring R and let I be a monomial idea (so I is generated by elements of the form x 1 e 1 ··· x d e d , where each e i is a nonnegative integer). The main results of this paper: (a) establish a practical formula which computes the monomial length of I when Rad( I ) = Rad(( x 1 ,…, x d ) R ); (b) determine necessary and sufficient conditions for the intersection of finitely many monomial ideals to again be a monomial ideal; (c) show that if C , the set of all monomial ideals in R that contain I , is closed under finite intersections, then each ideal J in C has a unique decomposition as an irredundant finite intersection of ideals of the form ( x τ(1) a 1 ,…, x τ( h ) a h ) R , where τ is a permutation of {1,…, d }, h ∈ {1,…, d }, and a 1 ,…, a h are positive integers; and, (d) give additional results for certain form rings and Rees rings of R , related to the unique parametric decomposition theorem.