Timeline for Cyclic decomposition of an infinitely generated module
Current License: CC BY-SA 3.0
7 events
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| Apr 23, 2016 at 0:35 | review | First posts | |||
| Apr 23, 2016 at 1:57 | |||||
| Apr 4, 2016 at 13:55 | comment | added | Mark Wildon | I think this is a reasonable question, but even the behaviour of abelian groups (i.e. $\mathbb{Z}$-modules) shows the situation is far more complicated. Some examples to bear in mind are the divisible Prufer groups $\lim \mathbb{Z}/p^n \mathbb{Z}$ (direct limit), the $p$-adic integers $\mathbb{Z}_p$, subgroups of $\mathbb{Q}$ such as $\{ n/2^i3^j : i,j \in \mathbb{N}_0, n \in \mathbb{Z} \}$ and the Baer--Specker group. None of these has a vector space direct summand. | |
| Apr 4, 2016 at 11:06 | history | edited | Bedovlat | CC BY-SA 3.0 |
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| Apr 3, 2016 at 23:03 | comment | added | Bedovlat | Thanks for the comment. A good one, actually. This is the situation where the module is non cyclic yet indecomposable. For some reasons I haven't met this in the examples I have in mind. I have to think about it. In view of this my question is probably either trivial or needs modification. | |
| Apr 3, 2016 at 22:41 | comment | added | Benjamin Steinberg | Q (the rationals) cannot be written as a direct sum of cyclic Z-modules. | |
| Apr 3, 2016 at 22:24 | history | edited | Bedovlat |
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| Apr 3, 2016 at 22:06 | history | asked | Bedovlat | CC BY-SA 3.0 |