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Ideal class group: History, History and origin of the ideal class group & Examples of ideal class groups

In mathematics, the ideal class group (or class group) of an algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle J_{K}/P_{K}} where J K {\displaystyle J_{K}} is the group of fractional ideals of the ring of integers of K {\displaystyle K} , and P K {\displaystyle P_{K}} is its subgroup of principal ideals. The class…

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Ideal class group topic overview

The analysis highlights History, History and origin of the ideal class group and Examples of ideal class groups as prominent areas in the source structure around Ideal class group.

Related topics
90
Source areas
7
Connected nodes
97
Extracted relationships
42
Concept neighborhoods
56
Bridge connections
97

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Overview · 25 topics
History and origin of the ideal class group · 22 topics
Examples of ideal class groups · 18 topics
Definition · 7 topics
Properties · 7 topics
Connections to class field theory · 6 topics
Relation with the group of units · 5 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

History and origin of the ideal class group

Definition

Properties

Relation with the group of units

Examples of ideal class groups

Connections to class field theory

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Ideal class group connects Entity context

The extracted context around Ideal class group shows recurring relationship patterns in the source. For example, Ideal class group → Carl Friedrich Gauss, Fermat, Fermat's Last Theorem, Ideal, It, Kummer, Kummer's, Later Ernst Kummer, Out, These, This, We Another extracted example is Ideal class group → Dedekind, However, Ideal, If, IJ, In, It, The, Thus. Use these groups to spot repeated connection types before inspecting the individual relationships.

Ideal class group

Top relations

related to history · 12
Ideal class group → Carl Friedrich Gauss, Fermat, Fermat's Last Theorem, Ideal, It, Kummer, Kummer's, Later Ernst Kummer, Out, These, This, We
related to Definition · 9
Ideal class group → Dedekind, However, Ideal, If, IJ, In, It, The, Thus
related to Examples of ideal class groups · 6
Ideal class group → Eisenstein, Euclidean, Gaussian, If, It, The
related to Connections to class field theory · 5
Ideal class group → Class, Every, Galois, Hilbert, The Hilbert
related to Properties · 5
Ideal class group → But, Dedekind, In, The, This
related to Relation with the group of units · 5
Ideal class group → Dedekind, Define, It, The, This

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

ideal class displaystyle group number integers ring principal domain field dedekind algebraic ideals sqrt fields mathbb unique factorization theory classes

Ideal class group relationships Subject–Predicate–Object triples

TTTA extracted 42 structured relationships around Ideal class group. Examples in this analysis include Ideal class group → related to Connections to class field theory → Class and Ideal class group → related to Connections to class field theory → Galois. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Ideal class grouprelated to Connections to class field theoryClass0.60section
Ideal class grouprelated to Connections to class field theoryGalois0.60section
Ideal class grouprelated to Connections to class field theoryHilbert0.60section
Ideal class grouprelated to Connections to class field theoryThe Hilbert0.60section
Ideal class grouprelated to Connections to class field theoryEvery0.60section
Ideal class grouprelated to DefinitionIf0.60section
Ideal class grouprelated to DefinitionIt0.60section
Ideal class grouprelated to DefinitionThe0.60section
Ideal class grouprelated to DefinitionIdeal0.60section
Ideal class grouprelated to DefinitionIJ0.60section
Ideal class grouprelated to DefinitionThus0.60section
Ideal class grouprelated to DefinitionIn0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Ideal class group bring nearby vocabulary together. In this analysis, examples include Group, Ideal and Displaystyle. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Ideal class group
    • Group
    • Ideal
    • Displaystyle
    • Principal
    • Domain
    • Dedekind
    • Ideals
    • Every
    • Algebraic
    • Classes
    • Ring
    • Number
  • ideal class group
    • Group
    • Ideal
    • Number
    • Displaystyle
    • Principal
    • Domain
    • Dedekind
    • Ring
    • Ideals
    • Integers
    • Field
    • Every
  • algebraic number field
    • Integers
    • Number
    • Ring
    • Field
    • Abelian
    • Theory
    • Group
    • Class
    • Example
    • Properties
    • Principal
    • Also
  • quotient group
    • Ideal
    • Displaystyle
    • Domain
    • Dedekind
    • Principal
    • Field
    • Algebraic
    • Number
    • Abelian
    • Fact
    • Ring
    • Ideals
  • group
    • Ideal
    • Displaystyle
    • Domain
    • Dedekind
    • Principal
    • Field
    • Algebraic
    • Number
    • Abelian
    • Fact
    • Ring
    • Ideals
  • ring of integers
    • Ring
    • Number
    • Rings
    • Domain
    • Mathbb
    • Unique
    • Trivial
    • Principal
    • Every
    • Dedekind
    • Sqrt
    • Domains
  • unique factorization
    • Factorization
    • Unique
    • Domains
    • Ring
    • Dedekind
    • Domain
    • Rings
    • Integers
    • Every
    • Principal
    • Group
    • Class
  • dedekind domains
    • Domain
    • Group
    • Domains
    • Ideals
    • Rings
    • Factorization
    • Ideal
    • Unique
    • Every
    • Principal
    • Properties
    • Elements

Connections between topic areas Semantic bridges

For Ideal class group, one of the stronger structural bridges in this analysis connects Ideal class group with Overview. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Ideal class group — Overview · splits 72 ⟂ 26
Ideal class group — History and origin of the ideal class group · splits 75 ⟂ 23
Ideal class group — Examples of ideal class groups · splits 79 ⟂ 19
Ideal class group — Definition · splits 90 ⟂ 8
Ideal class group — Properties · splits 90 ⟂ 8
Ideal class group — Connections to class field theory · splits 91 ⟂ 7
Ideal class group — Relation with the group of units · splits 92 ⟂ 6

Map overview Semantic statistics

Ideal class group

Nodes98
Edges97
Triples42
Avg. degree1.98
Density0.020408
Components1

Source & methodology

TTTA analyzes the structure around Ideal class group to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as History, History and origin of the ideal class group & Examples of ideal class groups, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Ideal class group · EN edition · Analysis: TopicsToTalkAbout

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