Talk:Cyclic module
Latest comment: 8 years ago by Quondum in topic Cyclic proper submodules of cyclic modules
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Silly cyclic modules
editIs there a name for modules M such that M ⊕ M is cyclic? Is there name for the largest n (depending on M) such that Mn is cyclic? JackSchmidt (talk) 22:03, 16 September 2008 (UTC)
- Good question! It looks a bit like P. M. Cohn type stuff, doesn't it? Actually, I don't think that this largest integer always exists; consider the ring in Invariant basis number#Examples. JoergenB (talk) 18:08, 24 September 2008 (UTC)
Cyclic proper submodules of cyclic modules
editIt seems like it might be worth mentioning under §Examples that a cyclic module MR over a ring R with nonzero zero divisors, a cyclic module may have a proper (cyclic) submodule MRa, where a is a (two-sided?) zero divisor of R. This might help with intuition for those not properly familiar with the topic, like me. —Quondum 14:19, 24 August 2016 (UTC)