On the finiteness of Gorenstein homological dimensions
Ioannis Emmanouil

Abstract. In this paper, we study certain properties of modules of finite Gorenstein pro-
jective, injective or flat dimensions. We examine conditions which imply that all Gorenstein
projective modules are Gorenstein flat and establish the balance of the Gorenstein-Tor-functor
for modules of finite Gorenstein projective dimension. We also examine the class of rings that
have finite Gorenstein global and weak dimensions and compute these dimensions, in terms
of certain cohomological invariants of the ring. Finally, we provide some examples of rings of
finite Gorenstein global and weak dimensions.