# Algebraic number field/Related Articles

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- Algebraic number [r]: A complex number that is a root of a polynomial with rational coefficients.
^{[e]} - Artin L-function [r]: A type of Dirichlet series associated to a linear representation ρ of a Galois group G.
^{[e]} - Conductor of a number field [r]: Used in algebraic number theory; a modulus which determines the splitting of prime ideals.
^{[e]} - Dedekind domain [r]: A Noetherian domain, integrally closed in its field of fractions, of which every prime ideal is maximal.
^{[e]} - Dedekind zeta function [r]: Generalization of the Riemann zeta function to algebraic number fields.
^{[e]} - Different ideal [r]: An invariant attached to an extension of algebraic number fields which encodes ramification data.
^{[e]} - Discriminant of an algebraic number field [r]: An invariant attached to an extension of algebraic number fields which describes the geometric structure of the ring of integers and encodes ramification data.
^{[e]} - Elliptic curve [r]: An algebraic curve of genus one with a group structure; a one-dimensional abelian variety.
^{[e]} - Field theory (mathematics) [r]: A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on the familiar concepts of real number arithmetic.
^{[e]} - Integral closure [r]: The ring of elements of an extension of a ring which satisfy a monic polynomial over the base ring.
^{[e]} - KANT [r]: A computer algebra system for mathematicians interested in algebraic number theory.
^{[e]} - Modulus (algebraic number theory) [r]: A formal product of places of an algebraic number field, used to encode ramification data for abelian extensions of a number field.
^{[e]} - Monogenic field [r]: An algebraic number field for which the ring of integers is a polynomial ring.
^{[e]} - Number theory [r]: The study of integers and relations between them.
^{[e]} - Order (ring theory) [r]: A ring which is finitely generated as a
**Z**-module.^{[e]} - Ring (mathematics) [r]: Algebraic structure with two operations, combining an abelian group with a monoid.
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