Timeline for Presentation of finite modules with null annihilator
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2011 at 18:19 | comment | added | Mahdi Majidi-Zolbanin | Must assume $M$ is not free over $R/I$. | |
| Jun 29, 2011 at 17:44 | comment | added | Mahdi Majidi-Zolbanin | I came up with another class of counterexamples. Consider any module $M$ with a finite presentation $R^n\rightarrow R^m\rightarrow M\rightarrow0$, where $m\leq n$ and annihilator of $M$ is not zero. Let $I$ be the annihilator of $M$, and tensor the given presentation with $R/I$. The result is an example of an $R/I$-module $M$ whose annihilator over $R/I$ is $(0)$ but has a minimal presentation over $R/I$ with $m\leq n$. | |
| Jun 27, 2011 at 20:56 | vote | accept | Mahdi Majidi-Zolbanin | ||
| Jun 27, 2011 at 20:11 | comment | added | Mahdi Majidi-Zolbanin | Thank you Graham, nice example. And thank you Hailong for responding. | |
| Jun 27, 2011 at 20:07 | answer | added | Hailong Dao | timeline score: 2 | |
| Jun 27, 2011 at 19:34 | comment | added | Graham Leuschke | Write $(0)$ in $R$ as an intersection of ideals $I_i$, and resolve the direct sum of the $R/I_i$. Counterexamples will appear quickly. | |
| Jun 27, 2011 at 19:33 | history | edited | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |
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| Jun 27, 2011 at 18:55 | history | edited | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |
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| Jun 27, 2011 at 18:48 | history | asked | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |