Talk:Artinian module
From Wikipedia, the free encyclopedia
Why does every (nontrivial) descending chain of submodules of has the form , like in the article? This is clear for the quasicyclic groups , for each prime p, because every proper subgroup is finite and cyclic. But this does not hold for . Where's the information from, that is artinian as -module? I have a little doubt about that ;-)
I propose therefore to replace by 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)
References?--Cronholm144 04:21, 18 July 2007 (UTC)
- Added. I don't know where the counterexample comes from, though. Ryan Reich 13:19, 18 July 2007 (UTC)