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Abstract
Assume that R = ⨁
i∈ℕ0
R
i
is a homogeneous graded Noetherian ring, and that M is a ℤ-graded R-module, where ℕ0 (resp. ℤ) denote the set all non-negative integers (resp., integers). The set of all homogeneous attached prime ideals of the top nonvanishing local cohomology module of a finitely generated module M, , with respect to the irrelevant ideal R
+: =⨁
i≥1
R
i
and the set of associated primes of
is studied. The asymptotic behavior of
for s ≥ f(M) is discussed, where f(M) is the finiteness dimension of M. It is shown that
is tame if
is Artinian for all i > h.
ACKNOWLEDGMENTS
The first author would like to express his thanks to Professor Jürgen Herzog for his informative discussion about graded modules during his visit to Mathematics Department in University of Duisburg-Essen. The authors would like to thank the referee for her/his comments.
The research of the first author was in part supported from IPM (No. 84130212).
Notes
Communicated by I. Swanson.