Timeline for Extension of projective module
Current License: CC BY-SA 3.0
7 events
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| Jul 4, 2012 at 12:55 | comment | added | David White | In case it'll help the OP, I want to mention that my go-to source for questions like this is Lectures on Modules and Rings by T.Y. Lam. This argument appears on page 172 as Corollary 5.23. I assume the OP asked his question for a reason, and it might be useful to read this section of Lam to see if other questions he has are also answered. | |
| Jul 4, 2012 at 11:05 | comment | added | Anton Fonarev | @Fernando, this obviously happens as $pd_{\mathbf{Z}/4}(\mathbf{Z}/2)=\infty$. I've already put this assumption that I had in mind. | |
| Jul 4, 2012 at 10:59 | comment | added | Fernando Muro |
Counterexample: the ring $\mathbb{Z}/4$ and the extension $0\rightarrow \mathbb{Z}/2\rightarrow\mathbb{Z}/4\rightarrow\mathbb{Z}/2\rightarrow$.
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| Jul 4, 2012 at 10:58 | history | edited | Anton Fonarev | CC BY-SA 3.0 |
updated with respect to a-fortiori's comment
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| Jul 4, 2012 at 10:57 | comment | added | Anton Fonarev | @a-fortiori Sure, thanks for pointing this out. | |
| Jul 4, 2012 at 10:28 | comment | added | user2035 | It is also possible that $\mathrm{pd}_B(N)=0\ne\infty=\mathrm{pd}_B(M)$. | |
| Jul 4, 2012 at 10:10 | history | answered | Anton Fonarev | CC BY-SA 3.0 |