Algebraic Number Theory Link

is a major branch of number theory that uses the techniques of abstract algebra to study integers, rational numbers, and their generalizations. It primarily investigates properties of algebraic number fields —finite extensions of the rational numbers Qthe rational numbers —and their rings of integers . Core Concepts and Motivations

: In certain number rings, a single number can be factored into irreducibles in multiple ways. For example, in Algebraic Number Theory

: Numbers that are roots of monic polynomials with integer coefficients. is a major branch of number theory that

: Developed by Richard Dedekind, this theory "restores" unique factorization by looking at ideals rather than individual elements. Algebraic Number Theory