Cartan–eilenberg Fp-Injective Complexes

Abstract

In this article, we extend the notion of FP-injective modules to that of Cartan–Eilenberg complexes. We show that a complex $C$ is Cartan–Eilenberg FP-injective if and only if $C$ and $\text{Z}(C)$ are complexes consisting of FP-injective modules over right coherent rings. As an application, coherent rings are characterized in various ways, using Cartan–Eilenberg FP-injective and Cartan–Eilenberg flat complexes.

Cartan-Eilenberg Ding projective complexes

“…Recently, Enochs studied Cartan-Eilenberg projective and injective complexes, Cartan-Eilenberg Gorenstein injective complexes are also introduced and studied [5]. We also considered Cartan-Eilenberg FP-injective complexes in [9]. In this paper, our main purpose is to introduce and investigate the concept of Cartan-Eilenberg Ding projective complexes.…”