Abstract Algebra

These notes are intended to provide just a brief introduction to groups, rings, and fields together with applications to straightedge and compass constructions as well as the unsolvability of the general quintic equation by radicals.

References to text material such as “Exercise 2.2.5” all refer to Algebra: Abstract and Concrete, Edition 2.5, by Frederick M. Goodman.

1. Some Examples of Groups

2. Morphisms and Subgroups

3. Cosets, Quotients and Homomorphisms

4. Rings and Fields

5. Straightedge and Compass Constructions

6. Galois Groups and Solving Quintics