Timeline for Examples of completions and algebraic closures
Current License: CC BY-SA 2.5
3 events
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| Jan 21, 2010 at 8:40 | comment | added | Pete L. Clark | ...I should mention that in exchange for not saying "Krasner", Brian's handout pays close attention to what happens in positive characteristic. This needs a little more argument, since (and I didn't say this above) Krasner's Lemma is only true for separable polynomials. | |
| Jan 21, 2010 at 8:37 | comment | added | Pete L. Clark | Just a comment on this nice handout: it turns on the fact (so important in many applications of local fields) that if you have a polynomial with coefficients in the completion, you can approximate it coefficient-by-coefficient arbitrarily well by elements of the uncompleted field, and then a basic result says that if two polynomials over a complete field are sufficiently close in coefficients and one is irreducible, then so is the other and their splitting fields are isomorphic. What Brian does not say is that this has a name: <b>Krasner's Lemma</b>. | |
| Jan 21, 2010 at 7:32 | history | answered | Paul Ziegler | CC BY-SA 2.5 |