Summary of Chapter 7

Contents of sections

1. The structure ring
2. Constructions with rings
3. Domains and fields
4. Fields
5. Ideals
6. Residue class rings
7. Finite fields
8. Exercises

Overview of contents

Chapter 7 is about rings. Special rings are domains and fields. We describe various constructions for rings, domains and fields, like Cartesian products, intersections, polynomial rings, fields of fractions and quotient rings.

Finite fields are studied in detail. In particular, we show that every finite field is isomorphic to a field Z/pZ[X]/(f) for some prime number p and irreducible polynomial f in Z/pZ[X].