科研之友
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摘要
Let R = circle plus(n epsilon N0) R-n be a positively graded Noetherian commutative ring. Set R+ := circle plus(n epsilon N) R-n. Let N = circle plus(n epsilon Z) N-n be a nonzero finitely generated graded R-module. Here, N-0, N, and Z denote the set of non-negative, positive, and all integers, respectively. Let (P) denote the properties: (i) for all i epsilon N-0 and all n epsilon Z, the R-0-module H-I(i)(N)(n) is finitely generated, (ii) for all i epsilon N-0, end(H-I(i)(N)) < infinity, where end (T) = Sup {r vertical bar T-r not equal 0}.
In this note, we study the following question: For a graded ideal I contained in R+, when does H-I(i)(N) have the properties (P)? Further, we study the tameness of H-I(i) (N).
