Algebraic number theory

About “Algebraic number theory”

Algebraic number theory" by Jürgen Neukirch is a foundational text that applies the methods of abstract algebra to the study of integers, rational numbers, and their generalizations. It examines algebraic objects such as algebraic number fields, their rings of integers, finite fields, and function fields, focusing on properties like unique factorization, ideal behavior, and Galois groups. These concepts are used to address central questions in number theory, including the solvability of Diophantine equations.