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Congruence relation

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. Every congruence relation has a corresponding quotient…

Examples, Congruences of groups, and normal subgroups and ideals & Definition

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Examples

Modular arithmeticIntegersDivisibleRemainderAddition
14 related topics

Congruences of groups, and normal subgroups and ideals

Given anyReflexivityIfSymmetryAnd
9 related topics

Definition

ModulesSemigroupsLatticesWell-definedUniversal algebra
7 related topics

Relation with homomorphisms

HomomorphismHomomorphism of groupsLinear mapIf and only ifFirst isomorphism theorem
7 related topics

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Overview

Definition

Examples

Relation with homomorphisms

Congruences of groups, and normal subgroups and ideals

Universal algebra

Category theory

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Congruence relation

Nodes62
Edges61
Triples23
Avg. degree1.97
Density0.032258
Components1

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Congruence relation

Top relations

related to Category theory · 5
Congruence relation → Definition, Hom, In, RX, See Quotient
related to Congruences of groups, and normal subgroups and ideals · 3
Congruence relation → Given, If, In
related to Example: Groups · 3
Congruence relation → For, If, Together
related to Basic example · 2
Congruence relation → For, The
related to Example: Rings · 2
Congruence relation → For, When
related to General · 2
Congruence relation → In, The
related to Ideals of rings and the general case · 2
Congruence relation → But, Omega-groups
related to Relation with homomorphisms · 2
Congruence relation → By, If
related to Universal algebra · 2
Congruence relation → An, The

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Important terminology

congruence relation equivalence algebraic algebra displaystyle structure quotient classes elements ring group compatible groups example set given relations universal theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Congruence relationrelated to Basic exampleThe0.60section
Congruence relationrelated to Basic exampleFor0.60section
Congruence relationrelated to Category theoryIn0.60section
Congruence relationrelated to Category theoryRX0.60section
Congruence relationrelated to Category theoryHom0.60section
Congruence relationrelated to Category theorySee Quotient0.60section
Congruence relationrelated to Category theoryDefinition0.60section
Congruence relationrelated to Congruences of groups, and normal subgroups and idealsIn0.60section
Congruence relationrelated to Congruences of groups, and normal subgroups and idealsIf0.60section
Congruence relationrelated to Congruences of groups, and normal subgroups and idealsGiven0.60section
Congruence relationrelated to Example: GroupsFor0.60section
Congruence relationrelated to Example: GroupsIf0.60section

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