MA 561 - Modern Algebra I (Fall 2009)

Course taught by Uwe Nagel at the University of Kentucky.


Overview


Schedule

Time and Place: MWF, 10:00 - 10:50 am, CB 347

Exams:

  • Midterm exam (CB 347, Oct 16, 10:00 - 10:50 am)
  • Final exam (CB 347, Dec 14, 8:00 - 10:00 am)



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:

      1. Guiding problems
      2. Field extensions
      3. The degree of a field extension
      4. Algebraic field extensions
      5. Quotient rings and the homomorphism theorem
      6. Quotient fields
      7. Simple field extensions
      8. Divisibility in integral domains
      9. Factorial domains
      10. Prime and maximal ideals
      11. Polynomial rings over factorial domains
      12. Irreducibility criteria for polynomials



Homework




Literature