Gorenstein FP-Injective Dimension for Complexes

Abstract

This article is a continuous work of [17], where the coauthors introduced the notion of 𝒢-FP-injective R-modules. In this article, we define a notion of 𝒢-FP-injective dimension for complexes over left coherent rings. To investigate the relationships between 𝒢-FP-injective dimension and FP-injective dimension for complexes, the complete cohomology group bases on FP-injectives is given.

Key Words:

• Complete cohomology
• FP-injective module
• 𝒢-FP-injective module

2010 Mathematics Subject Classification:

• 16E05
• 18G20
• 18G35

ACKNOWLEDGMENTS

This research was partially supported by NSFC (11371187,\ 11301268,\ 11301486), Foundation of Zhejiang Educational Committee (Y201431705), and Jiangsu University of Technology of China (KYY14012, KYY13021). The authors would like to thank the referee for the helpful comments and suggestions.

Notes

Communicated by A. Facchini.