Graduate algebra reviewer
These are my review notes for the graduate algebra comprehensive exam at De La Salle University. These notes are mainly based on Aluffi's "Algebra: Chapter 0" and Hungerford's "Algebra".
This is a work in progress but will follow the following outline:
- Preliminaries (sets, functions, categories, etc.)
- Groups
- Basic definitions
- Homomorphisms and subgroups
- Quotient groups, the isomorphism theorems
- Group actions
- Sylow theorems
- Direct and semidirect products
- Free groups
- Rings and modules
- Fields and Galois theory