Multiplicative functions and homomorphisms

[ehrenfest]

Homework Statement

What is the difference between multiplicative functions and homomorphisms?

Homework Equations

The Attempt at a Solution

 

[ZioX]

Multiplicative functions: the product of the image is the image of the product. There is another definition requiring that the two elements must be relatively prime.

Homomorphisms: preserve structure between the domain and the codomain, this often requires a homomorphism to be multiplicative.

 

[ehrenfest]

I don't like that expression "preserve structure between the domain and the codomain" because it seems like it is not mathematical or even objective...

What does that mean in mathematical terms?

 

[ZioX]

In rings it means that multiplication and addition in each ring are very similar.