homomorphism en · NOUN
Pronunciation
- (US) audio
Etymology
From homo- + morphism.
Meanings
-
A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.
Definition 1.15. Let G and H be matrix Lie groups. A map #92;Phi from G to H is called a Lie group homomorphism if (1) #92;Phi is a group homomorphism and (2) #92;Phi is continuous.
2003, Brian C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer, page 17:A homomorphism of presheaves h#58;A#92;rightarrowB is a collection of homomorphisms h#95;U#58;A(U)#92;rightarrowB(U) commuting with restrictions.
1997, Glen E. Bredon, Sheaf Theory, 2nd edition, Springer, page 8:A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving.
1954, Kuo-Tsai Chen, Iterated Integrals and Exponential Homomorphisms, Proceedings of the London Mathematical Society, Reprinted in 2001, Philippe Tondeur (editor), Collected Papers of K.-T. Chen, Birkhäuser, page 54, This motivates a generalization, and exponential homomorphisms are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates.
- A similar appearance of two unrelated organisms or structures, as for example with fish and whales.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| homomorphisms | Number=Plur | lexicographic |
Coordinates
Deriveds
homomorphous · semigroup homomorphism · graph homomorphism · ring homomorphism · antihomomorphism · boundary homomorphism · connecting homomorphism
Hyponyms
automorphism (structure-preserving map between algebraic structures) · epimorphism (structure-preserving map between algebraic structures) · isomorphism (structure-preserving map between algebraic structures) · monomorphism (structure-preserving map between algebraic structures) · linear map (structure-preserving map between algebraic structures) · endomorphism (structure-preserving map between algebraic structures)
Relateds
convergent evolution · morphism
Translations (30)
da homomorfi (notion in mathematics) · fa همریختی (notion in mathematics) · ka ჰომომორფიზმი (notion in mathematics) · sl homomorfizem (notion in mathematics) · nl homomorfisme (notion in mathematics) · uk гомоморфізм (notion in mathematics) · is mótun (notion in mathematics) · ru гомоморфи́зм (notion in mathematics) · pt homomorfismo (notion in mathematics) · ar تَشَاكُل (notion in mathematics) · cs homomorfismus (notion in mathematics) · it omomorfismo (notion in mathematics) · vi phép đồng cấu (notion in mathematics) · sh homomorfizam (notion in mathematics) · bg хомоморфизъм (notion in mathematics) · pl homomorfizm (notion in mathematics) · fi homomorfismi (notion in mathematics) · ga homamorfacht (notion in mathematics) · de Homomorphismus (notion in mathematics) · es homomorfismo (notion in mathematics) · sv homomorfi (notion in mathematics) · pa ਹੋਮੋਮੌਰਫਿਜ਼ਮ (notion in mathematics) · is sammótun (notion in mathematics) · fr homomorphisme (notion in mathematics) · hi समाकारिता (notion in mathematics) · lt homomorfizmas (notion in mathematics) · hy հոմոմորֆիզմը (notion in mathematics) · el ομομορφισμός (notion in mathematics) · hu homomorfizmus (notion in mathematics) · sv homomorfism (notion in mathematics)