Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.

Algebraic number theory studies the arithmetic of algebraic number fields — the ring of integers in the number field, the ideals and units in the ring of integers, the extent to which unique …

I assume that students have taken a rst course in number theory and cer-tainly that they are familiar with modular arithmetic, as well as the statements of quadratic reciprocity.

Algebra & Number Theory 's inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry.

From the review: "The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is …

Algebraic number theory is the study of roots of polynomials with rational or integral coefficients. These numbers lie in algebraic structures with many similar properties to those of the integers.

In this course, we will study number fields and their rings of integers, and then use these to study the integers and Diophantine equations. Here are some things we want to understand:

Algebraic Number Theory generalizes many concepts from elementary number theory to larger number systems. It uses more advanced algebraic structures and techniques to solve …

Feb 14, 2026 · Historically, algebraic number theory developed as a set of tools for solving problems in elementary number theory, namely Diophantine equations (i.e., equations whose …

Algebraic number theory involves using techniques from (mostly commutative) algebra and finite group theory to gain a deeper understanding of number fields.