Rings and Fields

Part 1: Rings

1. Definition, examples, elementary properties
2. Ringhomomorphisms and Ideals
3. Zeroes of Polynomials
4. Prime Ideals and Maximal Ideals
5. Principal Ideal Domains, Unique Factorization Domains
6. Gaussian Integers, Euclidian Division Rings
7. Symmetric Polynomials: in the same document as Chapter 6.

Part 2: Fields

8. Prime Fields and Characteristic; Linear Algebra in Fields
9. Quadratic Extensions (Fun fact: in Dutch this is a “enkelvoudige uitbreiding”, which means “single extension” if you translate it literally.)
10. Finite and Algebraic Extensions
11. Splitting Fields
12. Finite Fields
13. Algebraically Closed Fields