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