MA 561 - Modern Algebra I (Fall 2003)

Course by Uwe Nagel at the University of Kentucky.

Overview

Schedule

MWF, 11:00 - 11:50, CB 238

Material

The first part of the course will be motivated by solving some classical constructability problems with straightedge and compass (e.g. trisecting an angle, construction of a regular n-gon). Later on further motivation will be drawn from investigating whether or not a formula for the roots of a polynomial exists.
The course will introduce the tools and concepts needed. Important key words are groups, rings, factorization, fields, and Galois theory.

CONTENTS:

2. Field extensions

3. The degree of a field extension

4. Algebraic field extensions

5. Quotient rings and the homomorphism theorem

6. Fields of fractions

7. Simple field extensions

8. Divisibility in rings

9. Factorial domains

10. Prime and maximal ideals

11. Polynomial rings over factorial domains

12. Irreducibility criteria for polynomials

13. Continuation of field homomorphisms and splitting fields

14. Some foundations of group theory

15. Galois extensions

Homework

Set 1 (pdf-file)
Set 2 (pdf-file)
Set 3 (pdf-file)
Set 4 (pdf-file)
Set 5 (pdf-file)
Set 6 (pdf-file)
Set 7 (pdf-file)
Set 8 (pdf-file)
Set 9 (pdf-file)
Set 10 (pdf-file)

Literature

D. S. Dummit, R. M. Foote, Abstract algebra (2nd edition).

M. Artin, Algebra.

T. H. Hungerford, Algebra.

S. Lang, Algebra.

Last Up-date: Dec. 8, 2003