Abstract Algebra I, Fall 2004
Instructor: Lucy Lifschitz
Syllabus
Homework 1 Do the following exercises from Vinberg
1.28 (page 11), 1.36 (page 12), 1.79, 1.80, 1.81 (page 33),
2.35, 2.36 (page 48), 2.44 (page 51)
Homework 2 Do the following exercises from Vinberg
3.63, 3.64, 3.65, 3.66 (page 108), 3.87 (page 117), 3.109 (page 131),
3.117, 3.118 (page 134).
1. Find the greatest common divisor of x^3 - x^2 + x - 1 and
x^4 + 3x^3 + 2x^2 + 3x + 1 over Q.
2. Prove that
a) x^2 + x + 1 is irreducible over Z_2
b) x^2 + 1 is irreducible over Z_7
Homework 3 Do the following exercises from Vinberg
4.46 (page 151), 4.58 (page 154), 4.60 (page 155), 4.84 (page 162),
4.90 (page 163), 4.112 (page 168), 4.117, 4.118 (page 169).
In addition, do the problems on this handout
Homework 3
Homework 4 Do the following exercises from Vinberg
5.24, 5.26 (page 178), 5.39 (page 181), 5.52 (page 187), 5.72 (page 194)
Test 2 Click here
Due December 1, 2004 in class
Final Exam: Tuesday, December 14, 1:30pm - 3:30pm