Algebraic number field/Related Articles: Difference between revisions
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Latest revision as of 11:01, 8 July 2024
- See also changes related to Algebraic number field, or pages that link to Algebraic number field or to this page or whose text contains "Algebraic number field".
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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. [e]
- Normal extension [r]: A field extension which contains all the roots of an irreducible polynomial if it contains one such root. [e]
- Field extension [r]: A field containing a given field as a subfield. [e]
- Abelian group [r]: A group in which the group operation is commutative. [e]
- Scheme (mathematics) [r]: Topological space together with commutative rings for all its open sets, which arises from 'glueing together' spectra (spaces of prime ideals) of commutative rings. [e]