ps2 - α be the real number such that α 4 = 5. (a) Show...

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Math 5c, Spring 10 Problem Set 2 Due Tuesday, April 13 4pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Splitting Field, Normal ±eld, Seperable and inseperable extensions § 13.4 5 § 13.5 11 1. Let f ( x ) F [ x ] be a polynomial of degree n . Let K be the splitting ±eld of f . Show that [ K : F ] divides n !. 2. Let
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Unformatted text preview: α be the real number such that α 4 = 5. (a) Show that Q ( iα 2 ) is normal over Q . (b) Show that Q ( α + iα ) is normal over Q ( iα 2 ). (c) Show that Q ( α + iα ) is not normal over Q . 3. Show that K is perfect if and only if every algebraic extension of K is seperable. 1...
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This note was uploaded on 07/19/2010 for the course MA 5c taught by Professor Susamaagarwala during the Spring '09 term at Caltech.

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