# homomorphism

## homomorphism

[hoh-muh-mawr-fiz-uhm, hom-uh-]
noun
1.
Biology. correspondence in form or external appearance but not in type of structure or origin.
2.
Botany. possession of perfect flowers of only one kind.
3.
Zoology. resemblance between the young and the adult.
4.
Mathematics. an into map between two sets that preserves relations between elements.
Also, homomorphy.

Origin:
1865–70; homo- + -morph + -ism

Dictionary.com Unabridged
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World English Dictionary
 homomorphism or homomorphy (ˌhəʊməʊˈmɔːfɪzəm, ˌhɒm-) —n biology similarity in form homomorphy or homomorphy —n homo'morphic or homomorphy —adj homo'morphous or homomorphy —adj

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Science Dictionary
 homomorphism   (hō'mə-môr'fĭz'əm, hŏm'ə-)  Pronunciation Key  A transformation of one set into another that preserves in the second set the operations between the members of the first set.
The American Heritage® Science Dictionary
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FOLDOC
Computing Dictionary

### homomorphism definition

mathematics
A map f between groups A and B is a homomorphism of A into B if
f(a1 * a2) = f(a1) * f(a2) for all a1, a2 in A.
where the *s are the respective group operations.
(2009-01-14)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Encyclopedia Britannica
Encyclopedia

homomorphism

(from Greek homoios morphe, "similar form"), a special correspondence between the members (elements) of two algebraic systems, such as two groups, two rings, or two fields. Two homomorphic systems have the same basic structure, and, while their elements and operations may appear entirely different, results on one system often apply as well to the other system. Thus, if a new system can be shown to be homomorphic to a known system, certain known features of one can be applied to the other, thereby simplifying the analysis of the new system