- norm of algebraic number
- норма алгебраического числа
English-Russian scientific dictionary. 2008.
norm of algebraic number
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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
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
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
Norm — or NORM may refer to: Contents 1 In academia 1.1 In mathematics 2 People 3 Miscellaneous 4 … Wikipedia
Algebraic structure — In algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations, satisfying some axioms. Abstract algebra is primarily the study of algebraic structures and their properties. The… … Wikipedia
Norm of an ideal — The norm of an ideal is defined in algebraic number theory. Let Ksubset L be two number fields with rings of integers O Ksubset O L. Suppose that the extension L/K is a Galois extension with :G= extstyle{Gal}(L/K). The norm of an ideal I of O L… … Wikipedia
Algebraic K-theory — 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
Norm form — In mathematics, a norm form is a homogeneous form in n variables constructed from the field norm of a field extension L/K of degree n. That is, writing N for the norm mapping to K, and selecting a basis e1, ..., en for L as a vector space over K … Wikipedia
Algebraic torus — In mathematics, an algebraic torus is a type of commutative affine algebraic group. These groups were named by analogy with the theory of tori in Lie group theory (see maximal torus). The theory of tori is in some sense opposite to that of… … Wikipedia
Norm variety — In mathematics, a norm variety is a particular type of algebraic variety V over a field F, introduced for the purposes of algebraic K theory by Voevodsky. The idea is to relate Milnor K theory of F to geometric objects V, having function fields… … Wikipedia
Norm residue isomorphism theorem — In the mathematical field of algebraic K theory, the norm residue isomorphism theorem is a long sought result whose complete proof was announced in 2009. It previously was known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato,… … Wikipedia
