M a 5c HOMEWORK 1 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote, unless stated otherwise. Page 519,4. Dene : Q[ 2] Q[ 2] a + b 2 a b 2,
Math 5c, Spring 10 Problem Set 5 Due May 4, 4 pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Galois groups of Composite elds and Cyclotomic extensions
14.4 4, 5 14.5 7, 13
M a 5c HOMEWORK 5 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote, unless stated otherwise. Page 595,4. Suppose f (x) = (x i ) L[x], and
Math 5c, Spring 10 Problem Set 1 Due Tuesday, April 4pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Field extensions, Algebraic closures, embeddings over a eld.
13.1 4 13.
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
Math 5c, Spring 10 Problem Set 2 Due Tuesday, April 20 4pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Galois extensions
14.1 4, 10 14.2 4, 9, 16
1
Math 5c, Spring 10 Problem Set 4 These problems are not due, but the material covered on them will be considered fair game for the midterm and nal exam. All numbered problems are from Dummit and Foote
Math5c, Spring 10 Problem Set 6 Due May 11, 4pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Galois groups of polynomials, Krummer extensions
14.6 16, 19, 38, 47 14.7 4
1
Math 5c, Spring 10 Problem Set 6 Due May 18, 4 pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Krummer extensions, Norms, traces, representations
14.2 17cd Let be a primiti
Math 5c, Spring 10 Problem Set 6 Due May 18, 4 pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Representations, canonical forms of matrices
18.1 3, 4, 6abc, 10, 12.2 1
1
Math 5c, Spring 10 Problem Set 9 Due May 3, 4 pm All numbered problems are from Dummit and Foote, Third Ed. Key Concepts: Shurs Lemma, Characters
18.1 9, 17, 19 18.3 4, 10
1
M a 5c HOMEWORK 2 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote. Page 545,5. Suppose K is a splitting eld over F for a collection of cf
M a 5c HOMEWORK 3 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote, unless stated otherwise. Page 567,4. Suppose there is an isomorphism :
Math 5c Midterm Due Wednesday, April 28, 4 pm Do the following 5 problems in 3 hours. You may cite any theorems proven in class or Dummit and Foote, but prove any material you use from other sources.
M a 5c HOMEWORK 6 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote, unless stated otherwise. Page 618,16. The polynomial is irreducible by
M a 5c HOMEWORK 7 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote, unless stated otherwise. Page 582,17. c) Gal( ) = cfw_1, , with (a + b
M a 5c HOMEWORK 8 SOLUTION
SPRING 09
The exercises are taken from the text, Abstract Algebra (third edition) by Dummit and Foote, unless stated otherwise. Page 852,3. Let : G F be a degree 1 represent