Research any topic before you write.

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

Brauer group

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer.

Products, Construction & The Brauer group of a scheme

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 Brauer 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

Construction

Examples

Severi–Brauer varieties

Cyclic algebras

The period-index problem

Class field theory

Galois cohomology

The Brauer group of a scheme

Relation to the Tate conjecture

The Brauer–Manin obstruction

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

Brauer group

Nodes144
Edges143
Triples70
Avg. degree1.99
Density0.013889
Components1

How this topic connects Entity context

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

Brauer group

Top relations

related to Examples · 16
Brauer group → Archimedean, Br, Brauer, BrR, C1, Equivalently, In, Let, More, Q/Z, Since, The Brauer, Then Br, There, Tsen's, Wedderburn's
related to Class field theory · 12
Brauer group → Archimedean, Br, Br Kv, Brauer, Hasse, If, If Kv, Kv, Q/Z, The, The Brauer, This
related to The Brauer group of a scheme · 10
Brauer group → Auslander, Azumaya, Brauer, Goldman, Grothendieck, In, The, The Brauer, There, Zariski
related to Galois cohomology · 9
Brauer group → Brauer, For, Gal, Galois, Gm, H2, Ks, Ks/K, More
related to Relation to the Tate conjecture · 9
Brauer group → Artin, Brauer, For, Indeed, Jacobian, Shafarevich, Tate, The, This
related to The Brauer–Manin obstruction · 7
Brauer group → Brauer, K-points, K-rational, Kv, Let, Manin, The Hasse
related to Severi–Brauer varieties · 6
Brauer group → Another, Brauer, For, Severi, Such, The
is a · 1
Brauer group → important birational invariant

Important terminology Word statistics

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

Important terminology

brauer group algebra field central simple algebras division degree projective scheme cyclic defined cohomology isomorphic hasse finite algebraic classes ring

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Brauer groupis aimportant birational invariant0.90text
Brauer grouprelated to Class field theoryThe Brauer0.60section
Brauer grouprelated to Class field theoryIf Kv0.60section
Brauer grouprelated to Class field theoryArchimedean0.60section
Brauer grouprelated to Class field theoryBr Kv0.60section
Brauer grouprelated to Class field theoryQ/Z0.60section
Brauer grouprelated to Class field theoryHasse0.60section
Brauer grouprelated to Class field theoryThe0.60section
Brauer grouprelated to Class field theoryIf0.60section
Brauer grouprelated to Class field theoryKv0.60section
Brauer grouprelated to Class field theoryThis0.60section
Brauer grouprelated to Class field theoryBrauer0.60section

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.