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单词 IntegralBasis
释义

integral basis


Let K be a number field. A set of algebraic integersMathworldPlanetmath{α1,,αs} is said to be an integral basis for Kif every γ in 𝒪K can be represented uniquelyas an integer linear combinationMathworldPlanetmath of {α1,,αs} (i.e. one can write γ=m1α1++msαs with m1,,ms(rational) integers).

If I is an ideal of 𝒪K, then {α1,,αs}I is said to be an integral basis for I if every element of I can be represented uniquely as an integer linear combination of {α1,,αs}.

(In the above, 𝒪K denotes the ring of algebraic integers of K.)

An integral basis for K over is a basis for K over .

Titleintegral basis
Canonical nameIntegralBasis
Date of creation2013-03-22 12:36:03
Last modified on2013-03-22 12:36:03
Ownerrspuzio (6075)
Last modified byrspuzio (6075)
Numerical id12
Authorrspuzio (6075)
Entry typeDefinition
Classificationmsc 11R04
Synonymminimal basis
Synonymminimal bases
Related topicAlgebraicInteger
Related topicIntegral
Related topicBasis
Related topicDiscriminantOfANumberField
Related topicConditionForPowerBasis
Related topicBasisOfIdealInAlgebraicNumberField
Related topicCanonicalFormOfElementOfNumberField
Definesintegral bases
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更新时间:2025/5/4 10:34:32