A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES

Let (R,m,k) be a Cohen-Macaulay complete local ring with the canonical module ω. The aim of this note, is to show that, under mild assumptions, the class of balanced big Cohen--Macaulay modules coincides with the one consisting of those modules admitting a right resolution by modules in Addω. This generalizes the well-known result for the class of maximal Cohen--Macaulay modules.