#field-theory

12. Field Theory and Polynomials

This volume studies fields, polynomials, and algebraic extensions. It provides the structural basis for algebraic number theory, algebraic geometry, and Galois theory. Part I. Fields and Basic Structures Chapter 1. Fields 1.1 Definition and examples 1.2 Subfields 1.3 Field homomorphisms 1.4 Characteristic of a field 1.5 Prime fields Chapter 2. Polynomial Rings 2.1 Polynomial definitions 2.2 Arithmetic of polynomials 2.3 Degree and leading coefficient 2.4 Division algorithm 2.5 Euclidean structure...