A NOTE ON BALANCED BIG COHEN–MACAULAY MODULES

Let $(R, m, k)$ be a Cohen-Macaulay complete local ring with the canonical module $\omega$. 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 $ Add\omega$. This generalizes the well-known result for the class of maximal Cohen--Macaulay modules.

کلیدواژه ها:

maximal Cohen-Macaulay modules ، balanced big Cohen-Macaulay modules ، canonical module