Timeline for Field constructions
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2012 at 16:25 | vote | accept | CommunityBot | moved from User.Id=10290 by developer User.Id=35285 | |
| Mar 14, 2012 at 10:11 | comment | added | Martin Brandenburg | I think this question is quite vague. | |
| Mar 14, 2012 at 6:39 | history | edited | user10290 | CC BY-SA 3.0 |
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| Mar 14, 2012 at 6:12 | answer | added | Denis Serre | timeline score: 1 | |
| Mar 14, 2012 at 1:44 | answer | added | Andrew Stout | timeline score: 5 | |
| Mar 14, 2012 at 1:21 | comment | added | KConrad | You really should read about Witt vectors, as Tom suggests. Although the construction in my previous comment leads to a (nonconstructive) field of char. 0 out of infinitely many fields of different positive characteristics, Witt vectors are a mathematically more significant way to create fields (well, domains) of characteristic 0 out of finite fields in a good (= functorial) manner. | |
| Mar 14, 2012 at 1:19 | comment | added | KConrad | Since you allow products of fields, consider $A= \prod_{p} {\mathbf Z}/p{\mathbf Z}$. This ring has characteristic 0: for no positive integer $n$ does $n=0$ in A. Let I be the ideal of elements of A which have finitely many nonzero coordinates. By Zorn's lemma, I is contained in a maximal ideal M of A. What's the characteristic of the field A/M? If it were a prime $p$ then $p=0$ in A/M, so $p$ is in M. But as a (diagonal) sequence in A, $p$ has all but one nonzero coordinate. Use this and the fact that I is in M to show 1 is in M, which is a contradiction. So char(A/M) = 0. | |
| Mar 14, 2012 at 0:46 | history | edited | user10290 | CC BY-SA 3.0 |
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| Mar 14, 2012 at 0:43 | comment | added | Tom Goodwillie | How about Witt vectors? | |
| Mar 14, 2012 at 0:41 | answer | added | Barry | timeline score: 3 | |
| Mar 14, 2012 at 0:37 | history | asked | user10290 | CC BY-SA 3.0 |