On the Degree of Hilbert Polynomials of Derived Functors

被引：0

作者：

Saremi, H. ^{[1
]}

Mafi, A. ^{[2
]}

机构：

[1] Islamic Azad Univ, Dept Math, Sanandaj Branch, POB 618, Sanandaj, Iran

[2] Univ Kurdistan, Dept Math, POB 416, Sanandaj, Iran

来源：

MATHEMATICAL NOTES | 2019年 / 106卷 / 3-4期

关键词：

Hilbert-Samuel polynomial; derived functors; MODULES; POWERS; DEPTH;

D O I：

10.1134/S0001434619090116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a d-dimensional Cohen-Macaulay local ring (R,m), let I be an m-primary ideal, and let J be a minimal reduction ideal of I. If M is a maximal Cohen-Macaulay R-module, then, for n large enough and 1 <= i <= d, the lengths of the modules Ext(R)i(R/J,M/InM) and ToriR(R/J,M/InM) are polynomials of degree d - 1. It is also shown that deg beta(R)(i)(M/InM)=deg mu(i)(R)(M/(IM)-M-n)=d - 1 where beta(R)(i) (center dot) and mu(i)(R) (center dot) are the ith Betti number and the ith Bass number, respectively.

引用

页码：423 / 428

页数：6

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