Timeline for Ext of cyclic module
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 8, 2012 at 22:34 | comment | added | Sándor Kovács | Dear Hailong, no problem at all and I didn't mean to fish for compliments or criticize your comment. I just wanted to explain my confusion. When I read "this fails" I thought you meant that my example does. And it's not at all a surprising example anyway, so it's not a big deal. Cheers! | |
| Aug 8, 2012 at 21:12 | comment | added | Hailong Dao | Dear Sándor, sorry for my poor use of language. Of course, it is useful to have a counter-example in the general case, I thought I would just point out the most obvious one. +1 to your nice examples! Cheers! | |
| Aug 8, 2012 at 21:07 | comment | added | Sándor Kovács | I see. You probably meant "it fails" and not "this fails"... Also, this is a series of not-entirely-obvious examples for any dimension larger than $1$. I figured that it might be more interesting to give an example where not every module is projective in case someone is thinking about trying to find the most general conditions under which the original statement may hold... | |
| Aug 8, 2012 at 20:58 | comment | added | Hailong Dao | Dear Sándor, I just meant that there is a simple counter example when the dimension is not $1$. | |
| Aug 8, 2012 at 20:57 | comment | added | Sándor Kovács | @Hailong, could you be more specific about what you mean? I believe $k$ does not have dimension at least $2$. | |
| Aug 8, 2012 at 20:34 | comment | added | Hailong Dao | In general this fails even when $R=k$. | |
| Aug 8, 2012 at 20:21 | history | answered | Sándor Kovács | CC BY-SA 3.0 |