LAUSR

Abstract Krause [19] has proved that the homotopy category K ( R - PureProj ) of pure projective modules over an associative ring R is compactly generated and equivalent to the Verdier quotient K ( R ) / T ( R ) , where T ( R ) is the triangulated subcategory of the homotopy category K ( R ) consisting of the pure acyclic complexes. We provide an alternative proof of this result. When restricted to the homotopy category of projective modules, this equivalence reduces to that obtained by Neeman [26] . As an application of this description of K ( R -PureProj ) , we show that the K-flat complexes defined by Spaltenstein [29] are, up to homotopy equivalence, the filtered colimits of K-projective complexes of pure projective modules.