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Dirichlet's unit theorem

In mathematics, Dirichlet's unit theorem is a basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet. It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a positive real number that determines how "dense" the units are.

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The regulator

Higher regulators

Stark regulator

P-adic regulator

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Dirichlet's unit theorem

Nodes49
Edges48
Triples11
Avg. degree1.96
Density0.040816
Components1

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Dirichlet's unit theorem

Top relations

related to The regulator · 10
Dirichlet's unit theorem → Archimedean, Dirichlet's, For, It, Nj, Suppose, The, Then, There, This
is a · 1
Dirichlet's unit theorem → basic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet

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Important terminology

number units real field regulator rank displaystyle group quadratic unit mathbb fields algebraic theorem complex imaginary embeddings example determinant theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dirichlet's unit theoremis abasic result in algebraic number theory due to Peter Gustav Lejeune Dirichlet0.90text
Dirichlet's unit theoremrelated to The regulatorSuppose0.60section
Dirichlet's unit theoremrelated to The regulatorThere0.60section
Dirichlet's unit theoremrelated to The regulatorArchimedean0.60section
Dirichlet's unit theoremrelated to The regulatorFor0.60section
Dirichlet's unit theoremrelated to The regulatorNj0.60section
Dirichlet's unit theoremrelated to The regulatorThen0.60section
Dirichlet's unit theoremrelated to The regulatorThis0.60section
Dirichlet's unit theoremrelated to The regulatorThe0.60section
Dirichlet's unit theoremrelated to The regulatorIt0.60section
Dirichlet's unit theoremrelated to The regulatorDirichlet's0.60section

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