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I have a problem in my algebra class that says:

Prove that there are no ring homomorphisms from Z5 to Z7.

I have the following definition of ring homomorphism:

Let R and S be rings. A function R to S is a ring homomorphism if the following holds:

f(1R)=1S.

f(r1+r2)=f(r1)+f(r2) for all r1 and r2 in R.

f(r1r2)=f(r1)f(r2) for all r1 and r2 in R.

I've been thinking and wouldn't f(x)=0 work?

This is a problem in a published textbook so it doesn't make sense to me. Could anyone clue me in to where there might be a contradiction in the definition?

Thanks in anticipation. Mike.

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# Homework Help: There are no ring homomorphisms from Z5 to Z7

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