Ideals of analytic deviation one with respect to a Cohen-Macaulay module

被引：0

作者：

Ganesh S. Kadu

机构：

[1] IIT Bombay,Department of Mathematics

来源：

Indian Journal of Pure and Applied Mathematics | 2011年 / 42卷

关键词：

Blow-up algebra; analytic deviation; analytic spread; reductions; Cohen-Macaulay modules;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let (A, m) be a Cohen-Macaulay local ring, M a Cohen-Macaulay A-module of dimension d ≥ 1 and I a proper ideal of analytic deviation one with respect to M. In this paper we study the Cohen-Macaulayness of associated graded module of a Cohen-Macaulay module. We show that if I is generically a complete intersection of analytic deviation one and reduction number at most one with respect to M then GI (M) is Cohen-Macaulay. When analytic spread of I with respect to M equals d we prove a similar result when reduction number of an ideal is atmost two.

引用

页码：73 / 97

页数：24

共 20 条

[1] Brodmann M.(1979)Asymptotic stability of Ass( Proc. Math. Soc. 74 16-18
[2] Eisenbud D.(1983)) J. Algebra 81 202-224
[3] Huneke C.(1994)Cohen-Macaulay Rees algebras and their specialization Amer. J. Math. 116 905-919
[4] Goto S.(1996)On graded rings associated to analytic deviation one ideals Amer. J. Math. 118 1197-1213
[5] Huckaba S.(1992)Cohen-Macaulay graded rings associated to ideals Amer. J. Math. 114 367-403
[6] Goto S.(1993)Powers of ideals having small analytic deviation Trans. Amer. Math. Soc. 339 373-402
[7] Nakamura Y.(1996)Rees algebras of ideals having small analytic deviation Compositio Math. 103 7-29
[8] Nishida K.(2006)Artin-Nagata properties and Cohen-Macaulay associated graded rings Proc. Amer. Math. Soc. 134 3437-3444
[9] Huckaba S.(1978)On Burch’s inequality and a reduction system of a filtration Nagoya Math J. 72 93-101
[10] Huneke C.(undefined)Form rings and regular sequences undefined undefined undefined-undefined

← 1 2 →