Coherent Rings and Gorenstein FP-Injective Modules

Abstract

In this article, Gorenstein FP-injective modules are introduced and investigated. A left R-module M is called Gorenstein FP-injective if there is an exact sequence … → E ₁ → E ₀ → E ⁰ → E ¹ → … of FP-injective left R-modules with M = ker(E ⁰ → E ¹) such that Hom _R (P, −) leaves the sequence exact whenever P is a finitely presented left R-module with pd _R (P) < ∞. Some properties of Gorenstein FP-injective modules are obtained. Several well-known classes of rings are characterized in terms of Gorenstein FP-injective modules.

Key Words:

• Coherent ring
• Gorenstein FP-injective module
• Gorenstein flat module
• Gorenstein projective module
• Self-FP-injective

2010 Mathematics Subject Classification:

• 18G25
• 16D50
• 16E10
• 16E50

ACKNOWLEDGMENTS

The first author would like to thank Professor Najib Mahdou for his encouragement in writing this article. The authors would like to thank the referee for valuable suggestions and corrections, which have improved this article. This work was partially supported by NSFC (No. 11171240), and the Scientific Research Foundation of CUIT (No. KYTZ201201).

Notes

Communicated by I. Swanson.