Gorenstein dimensions of unbounded complexes and change of base (with an appendix by Driss Bennis)

被引：11

作者：

Christensen, Lars Winther ^{[1
]}

Koksal, Fatih ^{[2
]}

Liang, Li ^{[3
]}

机构：

[1] Texas Tech Univ, Dept Math & Stat, Lubbock, TX 79409 USA

[2] Lewis Univ, Dept Comp & Math Sci, Romeoville, IL 60446 USA

[3] Lanzhou Jiaotong Univ, Sch Math & Phys, Lanzhou 730070, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2017年 / 60卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Gorenstein injective dimension; faithfully flat co-base change; Gorenstein flat dimension; faithfully flat base change; MODULES;

D O I：

10.1007/s11425-015-0798-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a commutative ring R and a faithfully flat R-algebra S we prove, under mild extra assumptions, that an R-module M is Gorenstein flat if and only if the left S-module S aSu (R) M is Gorenstein flat, and that an R-module N is Gorenstein injective if and only if it is cotorsion and the left S-module Hom (R) (S,N) is Gorenstein injective. We apply these results to the study of Gorenstein homological dimensions of unbounded complexes. In particular, we prove two theorems on stability of these dimensions under faithfully flat (co-)base change.

引用

页码：401 / 420

页数：20