Abstract
In this note, some sufficient conditions are given for the equality Gid R RHom R (M, N) = G-dim R M + Gid R N to hold via vanishing of Tate cohomology. For instance, let R be a commutative Gorenstein local ring, and let M and N be finite R-modules. If one has for all i ∈ ℤ, then Gid R RHom R (M, N) = G-dim R M + Gid R N. In addition, some Auslander–Buchsbaum type width (depth) formulas are given.
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