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Group ring

In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of scalars is the given ring, and its basis is the set of elements of the given group. As a ring, its addition law is that of the free module and its multiplication extends "by linearity"…

Products, Group algebra over a finite group & Examples

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Overview

Definition

Examples

Some basic properties

Group algebra over a finite group

Group rings over an infinite group

Category theory

Filtration

Advanced semantic analysis

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Map overview Semantic statistics

Group ring

Nodes98
Edges97
Triples51
Avg. degree1.98
Density0.020408
Components1

How this topic connects Entity context

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Group ring

Top relations

related to References · 21
Group ring → Algebras, An, Bovdi, Curtis, César Polcino, EMS Press, Encyclopedia, February, Group, Interscience, Irving Reiner, ISBN, Mathematics, Passman, Representation, Sehgal, Springer, Sudarshan, The, Volume
related to Adjoint · 7
Group ring → Alg, Categorically, Grp, If, In, R-algebra, When
related to Group rings over an infinite group · 7
Group ring → In, Irving Kaplansky, Kaplansky, Much, The, This, Whether
related to Definition · 4
Group ring → Let, RG, The, To
related to Group algebra over a finite group · 4
Group ring → As, Group, That, The
related to Universal property · 4
Group ring → For, Let, R-algebra, The
is a · 2
Group ring → free module and at the same time a ring, generalization of a given group
related to Filtration · 2
Group ring → Coxeter, If

Important terminology Word statistics

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Important terminology

group ring algebra displaystyle finite field elements element given representations representation rings space groups case free vector order structure module

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Group ringis afree module and at the same time a ring0.90text
Group ringis ageneralization of a given group0.90text
Group ringrelated to AdjointCategorically0.60section
Group ringrelated to AdjointGrp0.60section
Group ringrelated to AdjointAlg0.60section
Group ringrelated to AdjointR-algebra0.60section
Group ringrelated to AdjointWhen0.60section
Group ringrelated to AdjointIn0.60section
Group ringrelated to AdjointIf0.60section
Group ringrelated to DefinitionLet0.60section
Group ringrelated to DefinitionThe0.60section
Group ringrelated to DefinitionRG0.60section

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