Pseudo Cohen–Macaulay and pseudo generalized Cohen–Macaulay modules

In this paper we study the structure of two classes of modules called pseudo Cohen–Macaulay and pseudo generalized Cohen–Macaulay modules. We also give a characterization for these modules in term of the Cohen–Macaulayness and generalized Cohen–Macaulayness. Then we apply this result to prove a cohomological characterization for sequentially Cohen–Macaulay and sequentially generalized Cohen–Macaulay modules.