Cotilting modules and Gorenstein homological dimensions

Abstract

For a dualizing module $D$ over a commutative Noetherian ring $R$ with identity, it is known that its Auslander class $\mathscr{A}_D\left(R\right)$ (respectively, Bass class $\mathscr{B}_D\left(R\right)$) is characterized as those $R$-modules with finite Gorenstein flat dimension (respectively, finite Gorenstein injective dimension). We establish an analogue of this result in the context of cotilting modules over general Noetherain rings.