##
Math 517 Spring 2003

**Section 65446, 9:00-9:50 MWF Taft Hall 216**

**Office Hours: MWF 12-1**

**Lawrence Ein
, 419 SEO, 3-2372, ein@uic.edu**

**Department of Mathematics, Statistics,
and Computer Science**
###
Table of Contents:

##
Description

**517 Abstract Algebra II**

**4 Hours.**

**Prerequisite: Math 516 or equivalent, or permission
of the instructor.**

**Text: Dummitt and Foote, Abstract Algebra, Prentice Hall**
**This is the basic graduate algebra course, the second course in a
sequence of two courses.**

**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 the second course.**

**The topics to be covered are:**

**Fields: Algebraic extensions, Galois theory, transcendental extensions**

**
Chapters 13-14**

**Commutatve Algebra: Hilbert's Nullstellensatz, primary decompositions**

**
;
integral extensions**

**
Chapters 15-16**

**Grading: There will be homework assignments every week, as well as
a final exam.**

##
**Homework**

HOMEWORK 1. Due Wednesday 1/22/03:
p. 499: 1, 6

p. 509: 3, 8, 9, 14, 16

HOMEWORK 2. Due Wednesday 1/29/03

p. 509: 18, 21, 22

p. 525: 1, 3; P. 531: 3, 5, 6, 8, 9, 10

HOMEWORK 3, Due 2/5/03

p. 535: 2, 4, 5, 7, 10, 13

p. 515: 1, 2, 4

p. 547: 4, 7, 8, 10

HOMEWORK 4, Due 2/12/03

p. 561: 1, 3, 7, 14, 15, 18, 21, 23, 24, 26, 29

HOMEWORK 5. Due 2/26/03

P. 583: 8, 10, 13

: p. 598: 2, 3, 5, 8, 10

HOMEWORK 6. Due 3/5/03

: P, 598: 13, 16, 18, 22, 27, 28, 29, 32, 34, 50, 51

HOMEWORK 7. Due 3/12/03

P. 601: 31, 33, 41 P. 618: 11, 13, 15, 19, 20

HOMEWORK 8, Due 3/26/03
P.625: 3, 6 p. 634: 2, 7, 12, 14, 19

HOMEWORK 9. Due 4/2/03
P.646 : 1, 3, 5, 8, 9, 10, 11, 24, 26, 33, 35

HOMEWORK 10. Due 4/9/03
p.661: 2, 8, 19, 37 p.675: 1, 8, 16, p. 693: 1, 6, 12, 15, 16

HOMEWORK 11. Due 4/16/03
P. 712: 2, 4, 15, 16 p.818: 5, 7, 9, 10, 18, 19, 20