ON PURE ACYCLIC COMPLEXES
IOANNIS EMMANOUIL
Abstract. 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 [14] 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 [18] on the pure projectivity of pure periodic modules.
Contents
0. Introduction 1
1. The relation to tensor products 3
2. The relation to finitely presented modules 5
3. The relation to pure projective modules 14
References 18