ON THE CATEGORY OF COFINITE MODULES WHICH IS ABELIAN

被引：42

作者：

Bahmanpour, Kamal ^{[1
]}

Naghipour, Reza ^{[2
,3
]}

Sedghi, Monireh ^{[4
]}

机构：

[1] Univ Mohaghegh Ardabili, Fac Math Sci, Dept Math, Ardebil 5619911367, Iran

[2] Univ Tabriz, Dept Math, Tabriz, Iran

[3] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

[4] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 142卷 / 04期

关键词：

Abelian category; arithmetic rank; cofinite module; Noetherian rings; LOCAL COHOMOLOGY MODULES; IDEALS;

D O I：

10.1090/S0002-9939-2014-11836-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R denote a commutative Noetherian (not necessarily local) ring and I an ideal of R of dimension one. The main purpose of this paper is to generalize, and to provide a short proof of, K. I. Kawasaki's theorem that the category M(R, I)(cof) of I-cofinite modules over a commutative Noetherian local ring R forms an Abelian subcategory of the category of all R-modules. Consequently, this assertion answers affirmatively the question raised by R. Hartshorne in his article Affine duality and cofiniteness [Invent. Math. 9 (1970), 145-164] for an ideal of dimension one in a commutative Noetherian ring R.

引用

页码：1101 / 1107

页数：7

共 12 条

[1] Cofiniteness of local cohomology modules for ideals of small dimension [J].