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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.
 Spring '09
 SusamaAgarwala
 Math, Algebra

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