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Module homomorphism

In algebra, a module homomorphism is a function between modules that preserves the module structures. Explicitly, if M and N are left modules over a ring R, then a function f : M → N {\displaystyle f:M\to N} is called an R-module homomorphism or an R-linear map if for any x, y in M and r in R,

Terminology, Examples & Exact sequences

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Overview

Terminology

Examples

A matrix representation

Defining

Operations

Exact sequences

Endomorphisms of finitely generated modules

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Map overview Semantic statistics

Module homomorphism

Nodes67
Edges66
Triples21
Avg. degree1.97
Density0.029851
Components1

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Module homomorphism

Top relations

related to A matrix representation · 5
Module homomorphism → End, In, Precisely, R-module, The
related to Defining · 5
Module homomorphism → In, More, R-modules, Suppose, Then
related to Exact sequences · 4
Module homomorphism → Consider, If, Rham, Such
is a · 3
Module homomorphism → function between modules that preserves the module structures, isomorphism, isomorphism if and only if it is an isomorphism between the underlying abelian groups.The isomorphism theorems hold for module homomorphisms.A module homomorphism from a module…
related to Terminology · 3
Module homomorphism → Conversely, In, The
related to Operations · 1
Module homomorphism → If

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Important terminology

displaystyle module homomorphism left operatorname ring called modules hom isomorphism right homomorphisms given commutative one end r-action additive endomorphism kernel

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Module homomorphismis afunction between modules that preserves the module structures0.90text
Module homomorphismis aisomorphism0.90text
Module homomorphismis aisomorphism if and only if it is an isomorphism between the underlying abelian groups.The isomorphism theorems hold for module homomorphisms.A module homomorphism from a module…0.90text
Module homomorphismrelated to A matrix representationThe0.60section
Module homomorphismrelated to A matrix representationPrecisely0.60section
Module homomorphismrelated to A matrix representationR-module0.60section
Module homomorphismrelated to A matrix representationIn0.60section
Module homomorphismrelated to A matrix representationEnd0.60section
Module homomorphismrelated to DefiningIn0.60section
Module homomorphismrelated to DefiningMore0.60section
Module homomorphismrelated to DefiningR-modules0.60section
Module homomorphismrelated to DefiningSuppose0.60section

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