homomorphism


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Related to homomorphism: homeomorphism, Automorphism

ho·mo·mor·phism

 (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.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

homomorphism

(ˌhəʊməʊˈmɔːfɪzəm; ˌhɒm-) or

homomorphy

n
(Biology) biology similarity in form
ˌhomoˈmorphic, ˌhomoˈmorphous adj
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

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.
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.homomorphism - similarity of form
similarity - the quality of being similar
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
homomorfismus
Homomorphismus
homomorfismi
homomorphisme
homomorfizam
homomorfizmus
omomorfismo
homomorfizmas
homomorfizm
homomorfizem
References in periodicals archive ?
The concept of Q-neutrosophic soft homomorphism (Q-NS hom) is defined and homomorphic image and preimage of a Q-NSG are investigated.
Before GSW scheme, since the LWE-based cryptosystem [15] itself supports additive homomorphism, the key point of constructing LWE-based FHE is to achieve multiplicative homomorphism.
A topological algebra (A, [[tau].sub.A]) is a left (right or two-sided) Segal topological algebra in a topological algebra (B, [[tau].sub.B]) via an algebra homomorphism f: A [right arrow] B if (1) [cl.sub.B](f(A)) = B;
Now in what follows, assume that [sigma], [tau] be two homomorphism on A.
We remark that there exists a natural group homomorphism [rho] : PBD(2,1) [right arrow] PGL(2, C), i.e., A [??] ([a.sub.ij]).
Define a homomorphism [[rho].sub.M] : (M [cross product] M, [mu] [cross product] [mu]) [right arrow] (Hom([M.sup.*], M), [iota]) by [[rho].sub.M](a [cross product] b)(f) = f(a)b, for all a, b [member of] M, f [member of] [M.sup.*], where [iota] : Hom([M.sup.*], M) [right arrow] Hom([M.sup.*], M) is the twisting given by [iota]([psi]) = [mu][psi][[mu].sup.*].
A function [phi] : V(G) [right arrow] V(H) is a homomorphism from G to H if it preserves edges, that is, if for any edge [u, v] of G, [[phi](u), [phi](v)] is an edge of H [12].
To take care of this issue, Davvaz [19, 31] introduced the idea of a set-valued homomorphism for rings and groups.
[32] divided image into several blocks and conducted data hiding in each block via additive homomorphism and pixel value ordering strategy.
The function [epsilon] : Z[[Q.sub.16]] [right arrow] Z given by [mathematical expression not reproducible] is a ring homomorphism. Let Q be the field of rational numbers, [M.sub.2](Q) the ring of 2 x 2 matrices with entries in Q, Q[[square root of (2)]] = {a + b [[square root of (2)]] | a, b [member of] Q}, H(Q[[[square root of (2)]]]) the quaternion field and [Q.sup.4] [direct sum] [M.sub.2] (Q) [direct sum] H(Q[[square root of (2)]]) the ring with component-wise addition and multiplication.
It introduces group actions early, and includes Hasse diagrams of posets and homomorphism diagrams, while introducing normal subgroups, quotient groups, and homomorphisms late.