Timeline for Irreducible elements in endomorphism rings
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 8, 2017 at 11:25 | comment | added | Dominic van der Zypen | Oh ok -- thanks Salvo, will correct this within the next days | |
| Mar 8, 2017 at 10:51 | comment | added | Salvo Tringali | (...) element $a \in H$ such that $a=xy$ for some $x, y \in H$ implies $x \in H^\times$ or $y \in H^\times$. | |
| Mar 8, 2017 at 10:46 | comment | added | Salvo Tringali | @DominicvanderZypen: I don't think this is the definition you want, since carrying it over to an arbitrary unital ring (that is, letting $g$ be reducible if there are non-units $h_1,h_2$ such that $g = h_1 h_2$, and irreducible otherwise) would imply that every unit of a Dedekind-finite ring $R$ is irreducible (see mathoverflow.net/questions/261982), and so is, in particular, the identity of $R$ (which is not so good a thing). Usually, we take an irreducible element in a unital ring $R$ to be an atom of its multiplicative monoid, and an atom in a monoid $H$ is a non-unit (...) | |
| Mar 8, 2017 at 10:30 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 166 characters in body
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| Mar 8, 2017 at 10:30 | comment | added | Dominic van der Zypen | That's right, I have included it. | |
| Mar 8, 2017 at 9:02 | vote | accept | Dominic van der Zypen | ||
| Mar 8, 2017 at 9:01 | answer | added | Salvo Tringali | timeline score: 8 | |
| Mar 8, 2017 at 8:55 | vote | accept | Dominic van der Zypen | ||
| Mar 8, 2017 at 9:02 | |||||
| Mar 8, 2017 at 8:33 | answer | added | Qiaochu Yuan | timeline score: 7 | |
| Mar 8, 2017 at 8:20 | comment | added | Włodzimierz Holsztyński | It wouldn't hurt to add your definition of the irreducible elements. | |
| Mar 8, 2017 at 7:58 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |