homomorphism

Noun

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Noun

**homomorphism** (*plural* homomorphisms)

- (
*algebra*) A structure-preserving map between two algebraic structures of the same type, such as group, ring, or vector spaces.*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.

- This motivates a generalization, and exponential
**1997**, Glen E. Bredon,*Sheaf Theory*, 2nd Edition, Springer, page 8 ↗,- A
*homomorphism**of presheaves*h : A \rightarrow B is a collection of**homomorphisms**h_U : A(U) \rightarrow B(U) commuting with restrictions.

- A
**2003**, Brian C. Hall,*Lie Groups, Lie Algebras, and Representations: An Elementary Introduction*, Springer, page 17 ↗,**Definition 1.15.***Let G and H be matrix Lie groups. A map \Phi from G to H is called a***Lie group homomorphism**if (1) \Phi is a group**homomorphism**and (2) \Phi is continuous.

- (
*biology*) A similar appearance of two unrelated organisms or structures.

- French: homomorphisme
- German: Homomorphismus
- Italian: omomorfismo
- Portuguese: homomorfismo
- Russian: гомоморфи́зм

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003