Timeline for A question of the book Elements of the representation theory of associative algebras volume 1
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2015 at 12:49 | comment | added | Xiaosong Peng | @ Dag Oskar Madsen Thank you again! And I think you're right now. | |
| Dec 3, 2015 at 11:57 | comment | added | Dag Oskar Madsen | @Person Sure. It's the left part of an exact sequence. | |
| Dec 3, 2015 at 11:54 | comment | added | Xiaosong Peng | @ Dag Oskar Madsen If you let u=[q,i]', is u a monomorphism? | |
| Dec 3, 2015 at 11:49 | comment | added | Dag Oskar Madsen | @Person I added more details. $P$ is the length $3$ indecomposable projective (you can think of it as the right hand coloumn) and $U=R/S \oplus P$. | |
| Dec 3, 2015 at 11:46 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
added more details
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| Dec 3, 2015 at 11:40 | comment | added | Xiaosong Peng | @ Dag Oskar Madsen Sorry,I can't understand your counterexample.Can you tell me what U and P is? | |
| Dec 3, 2015 at 11:08 | comment | added | Dag Oskar Madsen | @Penson If you want to prove $u$ factors through $P$, then you have to assume $U$ is indecomposable. See the counterexample I gave for decomposable $U$. | |
| Dec 3, 2015 at 11:04 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
clarified some points
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| Dec 3, 2015 at 6:52 | vote | accept | Xiaosong Peng | ||
| Dec 3, 2015 at 6:52 | comment | added | Xiaosong Peng | First ,thank you for answering my question .And I think it's also ture if U is decomposable.Because R is indecomposalbe,so u must map it to an indecomposable summand of U. We can replace U by its summand and get the result we want. Is it ok? | |
| Dec 2, 2015 at 17:45 | comment | added | Dag Oskar Madsen | Actually, the statement in green seems to be false in general if you don't assume $U$ is indecomposable. | |
| Dec 2, 2015 at 17:11 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
corrected diagram
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| Dec 2, 2015 at 17:01 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
added diagram
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| Dec 2, 2015 at 16:37 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
added 19 characters in body
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| Dec 2, 2015 at 16:28 | history | edited | Dag Oskar Madsen | CC BY-SA 3.0 |
added 823 characters in body
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| Dec 2, 2015 at 16:28 | history | undeleted | Dag Oskar Madsen | ||
| Dec 2, 2015 at 13:06 | history | deleted | Dag Oskar Madsen | via Vote | |
| Dec 2, 2015 at 12:59 | history | answered | Dag Oskar Madsen | CC BY-SA 3.0 |