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## Homework Statement

From ##\mathbb{Z}_3## to ##\mathbb{Z}_{15}##

## Homework Equations

## The Attempt at a Solution

I know how to do this if we assumed that the rings had to be unital. In that case, there can be no non-trivial homomorphism. However, in my book rings don't need unity, and so a homomorphism is defined only such that the operations are preserved. In this case, how do I show that there is no injective homomorphism?

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