Talk:Cyclic module

Silly cyclic modules

Is 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 $R\simeq R^{4}$ in Invariant basis number#Examples. JoergenB (talk) 18:08, 24 September 2008 (UTC)

Cyclic proper submodules of cyclic modules

It seems like it might be worth mentioning under §Examples that a cyclic module M_R over a ring R with nonzero zero divisors, a cyclic module may have a proper (cyclic) submodule M_Ra, 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)