On the Lowey length of modules of finite projective dimension—II.

Let (A , m) be a Cohen–Macaulay local ring of dimension d ≥ 1 . Suppose there exists be a non-zero A module M of finite length and finite projective dimension such that ℓ ℓ (M) , the Lowey length of M, is equal to λ (M) , the length of M. Then we show that necessarily A is at worst a hypersurface singularity. We also characterize Gorenstein local rings having a non-zero module M of finite length and finite projective dimension with ℓ ℓ (M) = λ (M) - 1 . [ABSTRACT FROM AUTHOR]