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homomorphism

[hoh-muh-mawr-fiz-uh m, hom-uh-] /ˌhoʊ məˈmɔr fɪz əm, ˌhɒm ə-/
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
1865-1870
1865-70; homo- + -morph + -ism
Related forms
homomorphous, adjective
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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Examples from the web for homomorphism
  • More technically, a homomorphism from a group to a group of matrices representation theory.
British Dictionary definitions for homomorphism

homomorphism

/ˌhəʊməʊˈmɔːfɪzəm; ˌhɒm-/
noun
1.
(biology) similarity in form
Derived Forms
homomorphic, homomorphous, adjective
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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homomorphism in Science
homomorphism
  (hō'mə-môr'fĭz'əm, hŏm'ə-)   
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
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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homomorphism in Technology

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 Article for 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

Learn more about homomorphism with a free trial on Britannica.com
Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.
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