Let $R$ be a local, noetherian ring of dimension $d$ and suppose it is generalized cohen-macaulay. Is it true that For any finitely generated $ R $-module $ M $, which is maximal generalized cohen-macaulay, $ \Omega^d M $ is maximal generalized cohen-macaulay.
Note that, $ M $(always noetherian over the local ring $ R $) is called generalized cohen-macaulay if for $ i = 0, 1,2 , ..., dim(M) - 1 $, $ H_{\frak m}^i(M) $ are noetherian modules.