Coherent Rings and Gorenstein FP-Injective Modules |
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| Authors: | Zenghui Gao Fanggui Wang |
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| Institution: | 1. College of Mathematics , Sichuan Normal University , Chengdu , China;2. College of Mathematics , Chengdu University of Information Technology , Chengdu , Sichuan , China gaozenghui@cuit.edu.cn;4. College of Mathematics , Sichuan Normal University , Chengdu , China |
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| 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. |
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| Keywords: | Coherent ring Gorenstein FP-injective module Gorenstein flat module Gorenstein projective module Self-FP-injective |
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