Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Ideal class group

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…

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

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Ideal class group. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. 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.

Map overview Semantic statistics

Ideal class group

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

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

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 Word statistics

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

Entity relationships Subject–Predicate–Object triples

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

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.