Timeline for If K/k is a finite normal extension of fields, is there always an intermediate field F such that F/k is purely inseparable and K/F is separable?
Current License: CC BY-SA 2.5
8 events
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| Feb 21, 2010 at 22:08 | comment | added | Zev Chonoles | I'll definitely check it out. Though McCarthy is hard to beat on price, I think - I got my copy for $4 :) | |
| Feb 21, 2010 at 21:26 | comment | added | Harry Gindi | A minor suggestion: Lang's chapters 5,6, 7, and 8 are really some of the best treatments of this subject. Chapter 5 is by far my favorite treatment of algebraic extensoins, and chapter 6 is an excellent treatment of Galois theory based on Artin's famous monograph (although covered with more modern machinery). I suggest you read them rather than McCarthy. | |
| Feb 21, 2010 at 21:22 | comment | added | Zev Chonoles | Ah, a very clever argument - and more general than the result McCarthy states! Thanks for your help! | |
| Feb 21, 2010 at 21:13 | vote | accept | Zev Chonoles | ||
| Feb 21, 2010 at 21:06 | comment | added | Harry Gindi | It's because if it's normal then you can construct it as a compositum of fields in a nice way using the automorphism groups. | |
| Feb 21, 2010 at 21:05 | history | edited | Harry Gindi | CC BY-SA 2.5 |
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| Feb 21, 2010 at 20:58 | comment | added | Zev Chonoles | No element in K generates a purely inseparable extension of F. That's the issue - I don't see why we couldn't have that an element in K generates a non-purely inseparable extension of F. | |
| Feb 21, 2010 at 20:53 | history | answered | Harry Gindi | CC BY-SA 2.5 |