Gorenstein projective and injective dimensions over Frobenius extensions

摘要

Let R subset of A be a Frobenius extension of rings. We prove that: (1) for any left A-module M, M-A is Gorenstein projective (injective) if and only if the underlying left R-module M-R is Gorenstein projective (injective). (2) if G-proj.dim(A)M