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dancergirlie
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Homework Statement
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?
Homework 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
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 =)