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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.
ACKNOWLEDGMENT
The first author was partly supported by National Natural Science Foundation of China (No. 11301242), and the second author was partly supported by National Natural Science Foundation of China (No. 11261050). It is a pleasure to thank the referee for thorough and useful comments.
Notes
Communicated by T. Albu.