homomorphism

ho·mo·mor·phism

H0258400 (hō′mə-môr′fĭz′əm, hŏm′ə-)n.1. Mathematics A transformation of one set into another that preserves in the second set the operations between the members of the first set.2. Biology Similarity of external form or appearance but not of structure or origin.3. Zoology A resemblance in form between the immature and adult stages of an animal.

ho′mo·mor′phic, ho′mo·mor′phous adj.

homomorphism

(ˌhəʊməʊˈmɔːfɪzəm; ˌhɒm-) or

homomorphy

n (Biology) biology similarity in form ˌhomoˈmorphic, ˌhomoˈmorphous adj

ho•mo•mor•phism

(ˌhoʊ məˈmɔr fɪz əm, ˌhɒm ə-)

also ho′mo•mor`phy,

n. 1. correspondence in form or external appearance. 2. possession of perfect flowers of only one kind. [1865–70] ho`mo•mor′phous, ho`mo•mor′phic, adj.

Thesaurus

Noun

homomorphism - similarity of formhomomorphysimilarity - the quality of being similar

Translations

homomorphism

[‚hä·mə′mȯr‚fiz·əm] (botany) Having perfect flowers consisting of only one type. (mathematics) A function between two algebraic systems of the same type which preserves the algebraic operations.

Homomorphism

a concept of mathematics and logic that first appeared in algebra but proved to be very important in understanding the structure and the area of possible applications of other branches of mathematics. The concept of homomorphism applies to a set of objects with prescribed operations (or relations). Thus, a homomorphism (homomorphic mapping) of a group G onto a group H is a mapping that associates to every element G∈G a definite element h∈H (the image of g) and satisfies the requirements that every element of H is the image of some element in G, and the image of the product (sum) of two elements in G is the product (sum) of their images. For example, the mapping that associates to an integer a the remainder when a is divided by a fixed positive integer m is a homomorphism of the group of integers (under addition) onto the group of residues modulo m. (The latter consists of m elements represented by the remainders 0, 1, . . . , m - 1.) The sum of two elements is represented by the sum of the corresponding remainders possibly diminished by m.

homomorphism

A map f between groups A and B is a homomorphism of A into Biff(a1 * a2) = f(a1) * f(a2) for all a1,a2 in A.

where the *s are the respective group operations.

homomorphism

ho·mo·mor·phism

homomorphism

homomorphy

ho•mo•mor•phism

also ho′mo•mor`phy,

homomorphism

homomorphism

Homomorphism

homomorphism

homomorphism

homomorphism

homomorphism

Synonyms for homomorphism

noun similarity of form

Synonyms

Related Words