Relative liftings Original Research Article

Let (Λ,m) be a complete Cohen-Macaulay local ring x a system of parameters of Λ and M a finite image. If image then there exists a maximal Cohen-Macaulay Λ-module L such that L/xL congruent with M by a result of Auslander-Ding-Solberg. Here we investigate the problem of finding a generalized Cohen-Macaulay Λ-module T such that T/xT congruent with M. If Λ is regular and (x) ≠ m then we hope that our procedure can be useful for some bundle constructions.