Normal Sally modules of rank one

JOURNAL OF ALGEBRA

卷:493

Article

Tran Thi Phuong¹ 

[1] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

关键词: Hilbert functions;    Hilbert coefficients;    Associated graded rings;    Rees algebras;    Sally modules;    Normal filtrations;    Serre condition;   

DOI  :  10.1016/j.jalgebra.2017.09.028

来源: Elsevier

【 摘 要 】

In this paper, we explore the structure of the normal Sally modules of rank one with respect to an m-primary ideal in a Nagata reduced local ring R which is not necessary Cohen-Macaulay. As an application of this result, when the base ring is Cohen-Macaulay analytically unramified, the extremal bound on the first normal Hilbert coefficient leads to the depth of the associated graded rings (G)over-bar with respect to a normal filtration is at least dim R-1 and (G)over-bar turns in to Cohen-Macaulay when the third normal Hilbert coefficient is vanished. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free