A Textbook of Algebraic Number Theory

This textbook provides a thorough exploration of algebraic number theory, covering significant theorems and their proofs, making it ideal for advanced students and researchers. A Textbook of Algebraic Number Theory is a valuable resource.

This self-contained and comprehensive textbook of algebraic number theory serves as an invaluable resource for advanced undergraduate and graduate students of mathematics. A Textbook of Algebraic Number Theory delves into proofs of nearly all fundamental theorems in the field, such as Dedekind’s theorem on the splitting of primes, Dirichlet’s unit theorem, and Minkowski’s convex body theorem. Additionally, it covers Dedekind’s discriminant theorem, Hermite’s theorem on discriminants, Dirichlet’s class number formula, and Dirichlet’s theorem regarding primes in arithmetic progressions. The book also presents research problems related to these results, along with the progress made in tackling each issue.

Adopting a classical approach rooted in Dedekind’s theory of ideals, A Textbook of Algebraic Number Theory aims to ignite the reader’s curiosity about ongoing research in this area. It not only establishes foundational results but also connects them to contemporary developments, thereby enhancing its relevance and stimulating thought. Historical notes are interspersed throughout the text, providing context and depth. The book is replete with numerous exercises and examples that reinforce the material, making it a significant asset for students and researchers alike.

Suitable for independent study, this textbook requires only a basic understanding of abstract algebra and elementary number theory. Its comprehensive nature and engaging presentation make it an essential addition to the library of anyone interested in algebraic number theory.