- 200

- 0

**1. The problem statement, all variables and given/known data**

Give an example of a ring R and a function f: R---->R such that f(a+b)=f(a)f(b) for all a,b in R. and f(a) is not the zero element for all a in R. Is your function a homomorphism?

**2. Relevant equations**

Let R and S be rings. A function f:R----->S is said to be a homomorphism if

f(a+b)=f(a) + f(b) and f(ab)=f(a)f(b) for all a,b in R

**3. The attempt at a solution**

Not really sure where to start here,

I was thinking about using Zn as my ring, perhaps with n as a prime number, so that way f(a) wouldn't be zero for any a. but i don't know what my function would be to satisfy that. Any help would be greatly appreciated =)