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