 algebraic number theory

The subfield of number theory where algebraic numbers are studied using algebra.
Wikipedia foundation.
Wikipedia foundation.
Algebraic number theory — In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number… … Wikipedia
Modulus (algebraic number theory) — In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle,[1] or extended ideal[2]) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to… … Wikipedia
List of algebraic number theory topics — This is a list of algebraic number theory topics. Contents 1 Basic topics 2 Important problems 3 General aspects 4 Class field theory … Wikipedia
Number theory — A Lehmer sieve an analog computer once used for finding primes and solving simple diophantine equations. Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers (the… … Wikipedia
Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… … Wikipedia
number theory — Math. the study of integers and their relation to one another. Also called theory of numbers. [1910 15] * * * Branch of mathematics concerned with properties of and relations among integers. It is a popular subject among amateur mathematicians… … Universalium
Algebraic Ktheory — In mathematics, algebraic K theory is an important part of homological algebra concerned with defining and applying a sequence Kn(R) of functors from rings to abelian groups, for all integers n. For historical reasons, the lower K groups K0 and… … Wikipedia
Computational number theory — In mathematics, computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations. The best known problem in the field is integer factorization. See also Computational… … Wikipedia
Algebraic number — In mathematics, an algebraic number is a complex number that is a root of a non zero polynomial in one variable with rational (or equivalently, integer) coefficients. Complex numbers such as pi that are not algebraic are said to be transcendental … Wikipedia
Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… … Wikipedia