Degenerations for modules over representation-finite algebras

Let A be a representation-finite algebra. We show that a finite dimensional A-module M degenerates to another A-module N if and only if the inequaliti es dim(K) Hom(A) (M; X) less than or equal to dim(K) Hom(A) (N; X) hold for all A-modules X. We prove also that if Ext(A)(1) (X; X) = 0 for any indeco mposable A-module X, then any degeneration of A-modules is given by a chain of short exact sequences.