Timeline for A relation between annihilators and ideals
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2018 at 10:49 | answer | added | Jesse Elliott | timeline score: 1 | |
| Feb 15, 2018 at 2:52 | comment | added | Sándor Kovács | I don't think there is any non-trivial condition that gives you this. On one hand you always have $J\subseteq \mathrm{Ann}(\mathrm{Ann}(J))$. On the other hand if $J\subsetneq \mathrm{Ann}(\mathrm{Ann}(J))$, then let $t\in \mathrm{Ann}(\mathrm{Ann}(J))\setminus J$ and $I=(t)$. Then this $I$ satisfies the condition, but the desired statement fails. The only way to guarantee this is that $J= \mathrm{Ann}(\mathrm{Ann}(J))$, but that's a trivial condition. | |
| Feb 14, 2018 at 19:12 | comment | added | rschwieb | I haven't been able to think of any nontrivial conditions (e.g. when $R$ is a dual ring, and $Ann(Ann(J))=J$ for all $J$.) Is there some motivation for a connection you could share? | |
| Feb 14, 2018 at 6:27 | comment | added | Viktor Vaughn | @AlecRhea An ideal is an $R$-module. | |
| Feb 14, 2018 at 6:21 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
Removed deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)
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| Feb 14, 2018 at 6:11 | comment | added | Alec Rhea | Is the existence of some $R$-module supposed to be implicit here? What is $J$ annihilating things in? I am not an expert in commutative algebra by any means, so forgive me if this is a common convention. | |
| Feb 14, 2018 at 5:49 | review | First posts | |||
| Feb 14, 2018 at 7:43 | |||||
| Feb 14, 2018 at 5:48 | history | asked | Nemool | CC BY-SA 3.0 |