## Math 517 Spring 2014

Section 16483,  10:00-10:50 MWF SEO 427
Office Hours: M W 11-12
Lawrence Ein , 419 SEO, 3-2372, ein@uic.edu
Department of Mathematics, Statistics, and Computer Science

• Description
• Homework
• ## Description

517 Abstract Algebra II
4 Hours.
Prerequisite: Math 516 or equivalent, or permission of the instructor.
Text: Paolo Aluffi, Algebra: Chapter 0, American Mathematical Society

This is the second basic graduate algebra course.
The courses are designed to cover the basic topics in algebra which would be needed
for a student who intends to pursue research not only in algebra but in various other areas.
For example, elements of commutative algebra which are needed for algebraic geometry
are covered in this second course.

The topics to be covered are:
Fields: Algebraic extensions, Galois theory, Transcendental Extensions
Chapters VII

Commutatve and Homological Algebra: Hilbert's Nullstellensatz, Primary Decompositions, Integral Extensions
Chapters VII- IX

Grading Policy: Homework (30%), Midterm Exam (20%) and Final (50%).

## Homework

HOMEWORK 1. Due Wednesday 1/22/14:

p. 397: 1.5, 1.6,1.7, 1.8. 1.11, 1.12, 1.13. 1.14, 1.15, 1.18, 1.24, 127. 1.27, 1.28, 1.29

p. 414: 2.2, 2.3, 2.16

HOMEWORK 2. Due Wednesday 1/29/14

p. 438: 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.10, 4.11, 4.12

HOMEWORK 3, Due 2/7/14

p. 452: 5.3, 5.4, 5.8, 5.9, 5.14, 5.15, 5.18, 5.21, 5.23

p. 466: 6.1, 6.3, 6.4, 6.5, 6.6

HOMEWORK 4, Due 2/14/14

p. 466: 6.7, 5.8, 6.9, 6.11, 6.15, 6.16, 6.17, 6.18, 6.19

p.480: 7.3, 7.4, 7.6, 7.8, 7.9, 7.10, 7.11, 7.12, 7.13

Take Home Exam Due 3/1/14

HOMEWORK 5. Due 2/28/14

P. 480: 7.14, 7.15, 7.16, 7.19

HOMEWORK 6. Due 3/14/14

P, 496: 1.2, 1.4, 1.5, 1.6, 1,.7, 1.9, 1.10, 1.11, 1.17,1.18, 1.19, 1.20, 1.21, 1.25

p.511: 2.2, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9

HOMEWORK 7. Due 4/4/14

P. 511: 2.16, 2.17, 2.19, 2.20, 2.21, 2.22, 2.23, 2.24, 2.25

p.520: 3,3, 3.6, 3.10, 3.14, 3.15

p.532: 4.4, 4.6, 4.7, 4.9, 4.11, 4.12

HOMEWORK 8, Due 4/11/14

P.532: 4.18, 4.19, 4.20, 4.22

p.543: 5.1, 5.2, 5.3, 5.4, 5.9, 5.12, 5.15, 5.17

p.555: 6.1, 6.4, 6.5, 5.5, 6.9, 6.10, 6.11, 6.12, 6.13, 6.14,

6.18, 6.21, 6.22

HOMEWORK 9. Due 4/18/14

P.574 : 1.4, 1.7, 1.13,1.14, 1.15, 1.17

p.589: 2.4, 2.14, 2.15, 2.17

p.602: 3,3, 3.4, 3.7, 3.11, 3.14, 3.15

HOMEWORK 10. Due 4/25/14

p.614: 4.1, 4.3, 4.6, 4.10, 4.11, 4.12, 4.13, 4.14

p.626: 5.1, 5.2, 5.5, 5.6, 5.8,5.9,5.10, 5.11, 5.12, 5.13, 5.14

HOMEWORK 12. Due 5/2/14

p. 658: 7.5, 7.6, 7.7, 7.9, 7.11, 7.12,7.13, 7.14, 7.15, 7.16, 7.18