homomorphism

plural homomorphisms

1. algebraA structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces.

   A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving.

   3 more examples

   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.

   1997, Glen E. Bredon, Sheaf Theory, 2nd edition, Springer, page 8

   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

2. biologyA similar appearance of two unrelated organisms or structures, as for example with fish and whales.