K-GORENSTEIN ALGEBRAS AND SYZYGY MODULES

We investigate for an artin algebra Lambda 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 Lambda which are k-Gorenstein for all k, that is, in a minimal injective resolution 0 --> Lambda --> I-0--> I-1-->...--> I-j -->... we have pd Lambda I-j less than or equal to 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 Lambda is k-Gorenstein for all k and id(lambda)Lambda < infinity, then id Lambda(lambda) < infinity.