Talk:Artinian module

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Why does every (nontrivial) descending chain of submodules of \mathbb{Q} / \mathbb{Z} has the form \langle1/ n_1 \rangle \supseteq \langle 1/ n_2 \rangle \supseteq ..., like in the article? This is clear for the quasicyclic groups \mathbb{Z}(p^{\infty}), for each prime p, because every proper subgroup is finite and cyclic. But this does not hold for \mathbb{Q} / \mathbb{Z}. Where's the information from, that \mathbb{Q} / \mathbb{Z} is artinian as \mathbb{Z}-module? I have a little doubt about that ;-)

I propose therefore to replace \mathbb{Q} / \mathbb{Z} by \mathbb{Z}(p^{\infty}) in the article. This gives certainly a counterexample for artinian => noetherian for modules. ---oo- 07:12, 16 September 2005 (UTC)

Since nobody vetoes, I've just corrected it. ;-) ---oo- 16:11, 18 September 2005 (UTC)

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