Homomorphism

Definitions

1. A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.
2. A similar appearance of two unrelated organisms or structures, as for example with fish and whales.

Equivalents

Examples

“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#58;A#92;rightarrowB is a collection of homomorphisms h#95;U#58;A(U)#92;rightarrowB(U) commuting with restrictions.”

“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.”

CEFR level