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Kernel (algebra)

In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism is a function that preserves the underlying algebraic structure in the domain to its image.

Definition, Group homomorphisms & Category theory

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Overview

Definition

Group homomorphisms

Ring homomorphisms

Linear maps

Quotient algebras

Kernel structures

Exact sequence

Universal algebra

Category theory

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Kernel (algebra)

Nodes131
Edges130
Triples0
Avg. degree1.98
Density0.015267
Components1

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Important terminology

displaystyle kernel homomorphism group ker quotient image ring set identity defined element category operation elements isomorphism algebra zero varphi kernels

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