Algebraic Number Theory Study Guide

Systematically review core concepts in algebraic number theory, including field extensions, ideal decomposition, and the classification of algebraic number fields, covering both basic theory and practical applications, and build a comprehensive knowledge framework from fundamentals to advanced levels.

Fundamental Theory of Algebraic Number Fields

Basic Concepts of Field Extensions and the Definition of Algebraic Integers

Factorization Theorem of Algebraic Integers Rings

Structural Analysis and Classification of Algebraic Number Fields

Structural Analysis of Algebraic Number Fields

Classification and Properties of Algebraic Number Fields

Properties of Ideal Decomposition and Class Number Theory

Properties of Ideal Decomposition

Class Number Theory Core Concepts

Tools and Methods for Algebraic Number Theory and Computational Techniques

Tools and Methods in Algebraic Number Theory

Algebraic Number Calculation Techniques