The so-called ’change-of-ring’ results are well-known expressions which present several connections between projective, injective and flat dimensions over the various base rings. In this note we extend these results to the Gorenstein dimensions over Cohen-Macaulay local rings.
We describe new classes of noetherian local rings R whose finitely generated modules M have the property that ToriR(M,M)=0 for i≫0 implies has finite projective dimension, or ExtRi(M,M)=0 dimension injective dimension.
