Timeline for Are there two non-isomorphic modules such that all the Hom-sets are isomorphic? [closed]
Current License: CC BY-SA 3.0
15 events
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| Dec 16, 2017 at 3:03 | review | Reopen votes | |||
| Dec 17, 2017 at 17:03 | |||||
| Dec 9, 2017 at 16:58 | review | Reopen votes | |||
| Dec 10, 2017 at 18:04 | |||||
| Dec 9, 2017 at 12:56 | history | edited | Marco D'Addezio | CC BY-SA 3.0 |
general improvements
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| Jul 7, 2012 at 9:38 | vote | accept | Marco D'Addezio | ||
| Jul 6, 2012 at 20:50 | history | closed |
Fernando Muro Vladimir Dotsenko Martin Brandenburg Dan Petersen user6976 |
too localized | |
| Jul 6, 2012 at 17:11 | comment | added | Anton Geraschenko | I've cleaned up this comment thread; the removed comments are copied at tea.mathoverflow.net/discussion/1403/some-cleaned-up-comments. | |
| Jul 6, 2012 at 13:19 | history | edited | Marco D'Addezio | CC BY-SA 3.0 |
edited title
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| Jul 6, 2012 at 11:52 | comment | added | user2035 | @Piotr: could you please explain the "boils down" a bit further? The implication "isomorphic duals" $\implies$ "all hom spaces isomorphic" seems to require some implication of the sort $2^\kappa=2^\lambda\implies \alpha^\kappa=\alpha^\lambda$ for all cardinals $\alpha$. Is this true? | |
| Jul 6, 2012 at 11:42 | history | edited | Marco D'Addezio | CC BY-SA 3.0 |
added 13 characters in body; edited title
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| Jul 6, 2012 at 11:36 | comment | added | Mark Grant | I suggest "Are modules isomorphic if their Hom-sets are all isomorphic?" (or something like that). | |
| Jul 6, 2012 at 11:25 | history | edited | Marco D'Addezio | CC BY-SA 3.0 |
edited body
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| Jul 6, 2012 at 4:23 | answer | added | Graham Leuschke | timeline score: 9 | |
| Jul 5, 2012 at 20:14 | comment | added | Piotr Pstrągowski | And if you do not assume the isomorphisms between Hom-sets to be natural, then for example over a field the question boils down to whether it is possible for two non-isomorphic vector spaces to have isomorphic duals. Over the field with two elements this is simply a question about the cardinality of power sets, which might very well be independant of ZFC. | |
| Jul 5, 2012 at 20:04 | comment | added | Piotr Pstrągowski | This follows from Yoneda lemma if you assume this isomorphisms are natural. | |
| Jul 5, 2012 at 19:52 | history | asked | Marco D'Addezio | CC BY-SA 3.0 |