GORENSTEIN INJECTIVE MODULES AND A GENERALIZATION OF ISCHEBECK FORMULA

被引：2

作者：

Sazeedeh, Reza ^{[1
,2
]}

机构：

[1] Urmia Univ, Dept Math, Orumiyeh, Iran

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

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2013年 / 12卷 / 04期

关键词：

Gorenstein injective module; Cohen-Macaulay ring; HOMOLOGICAL DIMENSIONS; RINGS;

D O I：

10.1142/S0219498812501976

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (R, m) be a commutative Noetherian local ring and let M and N be nonzero finitely generated R-modules of finite injective dimension and finite Gorenstein injective dimension, respectively. In this paper, we prove a generalization of Ischebeck formula, that is depth M-R + sup{i vertical bar Ext(R)(i) (M, N) not equal 0} = depth R.

引用

页数：10

共 14 条

[1]

Bass Hyman, 1963, Math. Z., V82, P8

[2]

Bruns W., 1998, CAMBRIDGE STUDIES AD, V39

[3] Transfer of Gorenstein dimensions along ring homomorphisms [J].

Christensen, Lars Winther ;

Sather-Wagstaff, Sean .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2010, 214 (06) :982-989

[4] GORENSTEIN INJECTIVE AND PROJECTIVE-MODULES [J].

ENOCHS, EE ;

JENDA, OMG .

MATHEMATISCHE ZEITSCHRIFT, 1995, 220 (04) :611-633

[5]

Fossum R., 1975, PUBL MATH-PARIS, V45, P193

[6] Cyclic modules of finite Gorenstein injective dimension and Gorenstein rings [J].

Foxby, Hans-Bjorn ;

Frankild, Anders J. .

ILLINOIS JOURNAL OF MATHEMATICS, 2007, 51 (01) :67-82

[7] MU-L IN A MINIMAL INJECTIVE RESOLUTION-II [J].

FOXBY, HB .

MATHEMATICA SCANDINAVICA, 1977, 41 (01) :19-44

[8] Gorenstein homological dimensions [J].

Holm, H .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2004, 189 (1-3) :167-193

[9] A DUALITY BETWEEN FUNCTOR-EXT AND FUNCTOR-TOR [J].

ISCHEBECK, F .

JOURNAL OF ALGEBRA, 1969, 11 (04) :510-+

[10]

Khatami L., 2003, PREPRINT

← 1 2 →