In persistence theory and practice, measuring distances between modules is central. The Wasserstein distances are the standard family of Lp distances (with 1≤p≤∞) for persistence modules. We give an algebraic formulation of these distances. For p=1 it generalizes to abelian categories and for arbitrary p it generalizes to Krull-Schmidt categories. These distances may be useful for the computation of distance between generalized persistence modules.