K-GORENSTEIN ALGEBRAS AND SYZYGY MODULES

We investigate for an artin algebra Lambda when categories of dth syzy gy modules are closed under extensions. In this case they are functori ally finite resolving, and have an associated cotilting module. We sho w 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 eq ual to j for all j. From this we get a correspondence between indecomp osable projective and indecomposable injective modules over these alge bras, which can be applied to prove that if Lambda is k-Gorenstein for all k and id(lambda)Lambda < infinity, then id Lambda(lambda) < infin ity.