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Dedekind domain

In mathematics, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are at least three other characterizations of Dedekind domains that…

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The prehistory of Dedekind domains

Integer solutionsPolynomial equationsRingsAlgebraic numbersInteger
32 related topics

Fractional ideals and the class group

Commutative semigroupMonoidSubgroupGroupIdeal class group
16 related topics

Some examples of Dedekind domains

Algebraic integersAffineAlgebraic curveCoordinate ringFraction field
12 related topics

Alternative definitions

Fractional idealIntegrally closedKrull dimensionKrull domainBourbaki
11 related topics

Topics to explore

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Overview

The prehistory of Dedekind domains

Alternative definitions

Some examples of Dedekind domains

Fractional ideals and the class group

Finitely generated modules over a Dedekind domain

Advanced semantic analysis

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Map overview Semantic statistics

Dedekind domain

Nodes97
Edges96
Triples46
Avg. degree1.98
Density0.020619
Components1

How this topic connects Entity context

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Dedekind domain

Top relations

related to history · 22
Dedekind domain → Alan Baker, At, By, Dedekind, Ernst Kummer, Especially, Euler, Fermat, Fermat's Last Theorem, For, Gabriel Lamé, Gauss, Gauss's, Harold Stark, However, In, Kummer, Kurt Heegner, PID, PIDs
related to Alternative definitions · 8
Dedekind domain → DD1, DD4, DD5, Dedekind, For, In, Thus, Which
related to Some examples of Dedekind domains · 8
Dedekind domain → All, As, DD4, Dedekind, Kummer, Noetherian, R/I, The
related to Finitely generated modules over a Dedekind domain · 6
Dedekind domain → Dedekind, In, Let, PID, Then, We
is a · 2
Dedekind domain → domain that either is a field, unique factorization domain

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Important terminology

dedekind domain displaystyle ideal ring field pid group fractional integral class one ideals domains algebraic integers principal fact generated rings

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dedekind domainis aunique factorization domain0.90text
Dedekind domainis adomain that either is a field0.90text
Dedekind domainrelated to Alternative definitionsFor0.60section
Dedekind domainrelated to Alternative definitionsThus0.60section
Dedekind domainrelated to Alternative definitionsDedekind0.60section
Dedekind domainrelated to Alternative definitionsDD10.60section
Dedekind domainrelated to Alternative definitionsDD50.60section
Dedekind domainrelated to Alternative definitionsWhich0.60section
Dedekind domainrelated to Alternative definitionsIn0.60section
Dedekind domainrelated to Alternative definitionsDD40.60section
Dedekind domainrelated to Finitely generated modules over a Dedekind domainIn0.60section
Dedekind domainrelated to Finitely generated modules over a Dedekind domainPID0.60section

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