FP-Injective Complexes

Abstract

In this article, FP-injective complexes are introduced and studied. We prove that ( ⊥ is a hereditary cotorsion theory if and only if R is a left coherent ring, where denotes the class of all FP-injective complexes of left R-modules. Simultaneously, we study the existence of FP-injective preenvelopes and FP-injective covers.

Weak Injective and Weak Flat Complexes

“…As one of important abelian categories, the category of complexes of modules has been studied by many authors (see, for example [1,4,13,10,11,17,25]), and many results of the category of modules which have been generalized to the category of complexes of modules. As we know, injective and flat complexes play important roles in the study of the category of complexes of modules, and a complex C is injective (resp.…”

“…flat) if and only if C is exact and Z m (C) is injective (resp. flat) as R-modules for any m ∈ Z; In [25,23], Liu et al introduced the notion of FP-injective complexes, they obtained many nice characterizations of them over coherent rings, and they showed that some properties of injective complexes have counterparts for FP-injective complexes. More recently, we introduced and investigated in [16,14] weak injective and weak flat modules, and generalized many results from coherent rings to arbitrary rings.…”