Gorenstein injective complexes of modules over Noetherian rings

JOURNAL OF ALGEBRA

卷:321

Article

Liu Zhongkui¹  Zhang Chunxia¹ 

[1] NW Normal Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

关键词: Gorenstein injective complex;    Gorenstein injective module;    Cover;    Gorenstein injective dimension;   

DOI  :  10.1016/j.jalgebra.2008.11.031

来源: Elsevier

【 摘 要 】

A complex C is called Gorenstein injective if there exists an exact sequence of complexes ... I-1 -> I-0 -> I-1 -> ... such that each I-i is injective, C = Ker(I-0 -> I-1) and the sequence remains exact when Hom(E. -) is applied to it for any injective complex E. We show that over a left Noetherian ring R, a complex C of left R-modules is Gorenstein injective if and only if C-m is Gorenstein injective in R-Mod for all m is an element of Z. Also Gorenstein injective dimensions of complexes are considered. (c) 2008 Published by Elsevier Inc.

【 授权许可】

Free