k-Gorenstein algebras and syzygy modules

We investigate for an artin algebra Λ when categories of dth syzygy modules are closed under extensions. In this case they are functorially finite resolving, and have an associated cotilting module. We show that this holds for all d for algebras Λ which are k-Gorenstein for all k, that is, in a minimal injective resolution 0 → Λ → I0 → I1 → ⋯ → Ij → ⋯ we have pdΛ Ij ⩽ j for all j. from this we get a correspondence between indecomposable projective and indecomposable injective modules over these algebras, which can be applied to prove that if Λ is k-Gorenstein for all k and idΛ Λ < ∞, then id ΛΛ < ∞.