A generalization of a theorem of Foxby

被引：4

作者：

Araya, Tokuji ^{[1
]}

Takahashi, Ryo ^{[2
]}

机构：

[1] Nara Univ Educ, Takabatake, Nara 6308528, Japan

[2] Shinshu Univ, Dept Math Sci, Fac Sci, Nagano 3908621, Japan

来源：

ARCHIV DER MATHEMATIK | 2009年 / 93卷 / 02期

关键词：

Projective dimension; Injective dimension; Semidualizing module; Gorenstein ring; COMPLEXES; MODULES;

D O I：

10.1007/s00013-009-0003-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, it is proved that a commutative noetherian local ring admitting a finitely generated module of finite projective and injective dimensions with respect to a semidualizing module is Gorenstein. This result recovers a celebrated theorem of Foxby.

引用

页码：123 / 127

页数：5

共 13 条

[1]

CHRISTENSEN L. W., 2000, Lect. Notes in Math., V1747

[2]

Christensen LW, 2008, P AM MATH SOC, V136, P479

[3] Semi-dualizing complexes and their Auslander categories [J].