j-Multiplicity and depth of associated graded modules

JOURNAL OF ALGEBRA

卷:379

Article

Polini, Claudia¹  Xie, Yu² 

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

关键词: Hilbert function;    Associated graded rings;    Cohen-Macaulay;    Hilbert coefficients;    j-Multiplicity;    Residual intersections;   

DOI  :  10.1016/j.jalgebra.2013.01.001

来源: Elsevier

【 摘 要 】

Let R be a Noetherian local ring. We define the minimal j-multiplicity and almost minimal j-multiplicity of an arbitrary R-ideal on any finite R-module. For any ideal I with minimal j-multiplicity or almost minimal j-multiplicity on a Cohen-Macaulay module M, we prove that under some residual conditions, the associated graded module gr(l)(M) is Cohen-Macaulay or almost Cohen-Macaulay, respectively. Our work generalizes the results for minimal multiplicity and almost minimal multiplicity obtained by Sally, Rossi, Valla, Wang, Huckaba, Elias, Corso, Polini, and Vaz Pinto. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free