Restricted Projective, Injective and Flat Complexes

Abstract

We introduce and study the notions of restricted projective, injective and flat complexes of modules. It is shown in the paper that a complex C of modules is restricted projective if and only if for each $$m\in \mathbb {Z}$$ the module $$C^{m}$$ is restricted projective. A similar result for restricted injective complexes is also given. As an application, we characterize the complex of strongly torsion-free modules introduced by Xu.