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On the local cohomology of minimax modules. (English) Zbl 1232.13009
Let \(\mathfrak a\) be an ideal of a commutative noetherian ring \(R\) and \(N\) a minimax \(R\)-module. The main result of this paper asserts that if either
a) \(\dim R/\mathfrak=1\),
b) \(\sup \{i\in \mathbb{N}_0| H_{\mathfrak a}^i(R)\neq 0\}=1\); or
c) \(\dim R\leq 2\),
then \(\mathrm{Ext}_R^j(R/\mathfrak a,H_{\mathfrak a}^i(N))\) is minimax for all \(i,j\in \mathbb{N}_0\). Recall that an \(R\)-module \(M\) is said to be minimax if it has a finitely generated submodule such that the quotient by it is Artinian.

MSC:
13D45 Local cohomology and commutative rings
13E99 Chain conditions, finiteness conditions in commutative ring theory
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