Abstract
Let R be a commutative Noetherian local ring, I a proper ideal of R, M, and N finitely generated R-modules. It is proved that f-depth(I + Ann(M), N) is the least integer r such that the generalized local cohomology module is not Artinian. Let r ≥ 0 be an integer. We also discuss the property that
is Artinian for all i ≥ r.
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ACKNOWLEDGMENT
The author is supported by the National Natural Science Foundation of China
Notes
Communicated by I. Swanson.