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 homomorphism of presheaves h:A→B is a collection of homomorphisms h_U:A(U)→B(U) commuting with restrictions.

Definition 1.15. Let G and H be matrix Lie groups. A map Φ from G to H is called a Lie group homomorphism if (1) Φ is a group homomorphism and (2) Φ is continuous.

Homomorphism

Meaning

Noun

Origin