Bass and Betti Numbers of a Module and Its Deficiency Modules

This paper aims to provide several relations between Bass and Betti numbers of a given module and its deficiency modules. Such relations and the tools used throughout allow us to generalize some results of Foxby, characterize Cohen–Macaulay modules in equidimensionality terms, study the Cohen–Macaulay and complete intersection properties of a ring, and furnish a case for the Auslander–Reiten conjecture.