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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
##### Keywords:
local cohomology modules; minimax modules
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