Timeline for Characterizing nilpotents in a ring by a universal property
Current License: CC BY-SA 2.5
14 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Feb 4, 2010 at 11:43 | vote | accept | Anweshi | ||
| Feb 4, 2010 at 11:30 | comment | added | Kevin Buzzard | @Pace: yeah but he explicitly said "B non-zero", for precisely this reason. | |
| Feb 3, 2010 at 21:26 | comment | added | Pace Nielsen | *make that "minimal ideal" | |
| Feb 3, 2010 at 21:24 | comment | added | Pace Nielsen | Pedantic ring theorist speaking: All elements (even nilpotents) can map to units. Just map to the zero ring. Pedantry aside: first of all we want every ideal $I$ of $R$, which contains the left and right annihilators of $a$, to NOT contain $a$ itself. This encompasses the situation of nilpotents and full idempotents. | |
| Feb 3, 2010 at 20:26 | comment | added | Kevin Buzzard | Yes and thanks to Matt too: I mean (1 0;0 0). Oh dear what a disastrous comment! I should have made it an answer, then I could have edited it! | |
| Feb 3, 2010 at 20:24 | comment | added | Kevin Buzzard | Yes, thanks darij. The argument is still OK but the "typo" is rather grotesque :-) | |
| Feb 3, 2010 at 20:02 | answer | added | Emerton | timeline score: 8 | |
| Feb 3, 2010 at 19:23 | answer | added | darij grinberg | timeline score: 1 | |
| Feb 3, 2010 at 19:11 | comment | added | darij grinberg | I think "a can't be contained in any prime ideal" should be "a is contained in every prime ideal" in your answer. | |
| Feb 3, 2010 at 19:06 | answer | added | Mariano Suárez-Álvarez | timeline score: -1 | |
| Feb 3, 2010 at 19:06 | comment | added | Kevin Buzzard | In the commutative case this is easy, right? a can't be contained in any prime ideal (consider A-->Frac(A/P)) and hence a is nilpotent by a standard result in ring theory. In the non-commutative case though I'm not so sure: what about (0 1;0 0) in M_2(C)? M_2(C) has no non-trivial 2-sided ideals so f must be injective and although this isn't a proof, I'm surely not far off. | |
| Feb 3, 2010 at 19:05 | history | edited | Anweshi | CC BY-SA 2.5 |
added 79 characters in body; deleted 4 characters in body; added 1 characters in body; edited tags
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| Feb 3, 2010 at 18:56 | history | asked | Anweshi | CC BY-SA 2.5 |