"Well a homomorphism applies to a group" Not so. The notion's far more general: https://en.wikipedia.org/wiki/Ring_homomorphism https://en.wikipedia.org/wiki/R

"Well a homomorphism applies to a group" Not so. The notion's far more general: https://en.wikipedia.org/wiki/Ring_homomorphism https://en.wikipedia.org/wiki/Ring_homomorphism This gives us a notion of homomorphisms between fields. https://en.wikipedia.org/wiki/Homomorphism https://en.wikipedia.org/wiki/Homomorphism for more general notions of homomorphisms.