On pure acyclic complexes

In this paper, we study the pure acyclic complexes of modules. We obtain several characterizations of these complexes, extending results that are known for the pure acyclic complexes of flat modules. In particular, we extend Neeman's characterization [18] of the pure acyclic complexes of flat modules in terms of complexes of projective modules, by considering more generally complexes of pure projective modules. As a consequence, we obtain Simson's result [22] on the pure projectivity of pure periodic modules.