Homomorphism

by rp

Sat Nov 13 1999 at 14:37:04

Given two sets with some structure imposed on it - for instance, a relation, or an operation, or an algebra - a homomorphism is a mapping from one to the other that preserves that structure.

E.g., the natural numbers can be mapped to the even natural numbers by the mapping x -> 2x; this is a homomorphism with respect to the usual ordering of numbers.

x -> 2^x is a homomorphism to map addition onto multiplication.

Isomorphisms are the most common.

I like it!

2 C!s

(definition)

by Webster 1913

Wed Dec 22 1999 at 0:11:20

Ho`mo*mor"phism (?), n. [See Homomorphous.]

1. Biol.

Same as Homomorphy.

2. Bot.

The possession, in one species of plants, of only one kind of flowers; -- opposed to heteromorphism, dimorphism, and trimorphism.

3. Zool.

The possession of but one kind of larvae or young, as in most insects.

<-- 4. (Math) A special type of mapping of one mathematical set into or onto another set . . . -->

I like it!

isomorphism	Homeomorphism	I'd like to thank my parents, Ayn Rand and God	semidirect product
category theory	R.E.M.	abstract algebra	tensor product
representations of groups	Lie algebras	isomorphism theorems	normal subgroup
group	general linear group	exact sequence	Generators and relations for groups
symmetry groups of the Platonic solids	first isomorphism theorem	monomorphism	lattice
kernel	A Weapon Called the Word	measure-preserving transformation