(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that a f: Z → R , n → n*1_{R}is a homomorphism of rings

2. Relevant equations

3. The attempt at a solution

I'm not sure how to exactly go about answering this question, but I'm going to try to start with the definition:

f(a+b) = f(a) + f(b)

f(a*b) = f(a) * f(b)

f(1_{Z}) = 1_{R}

Ok, so if I actually have a clue what the problem statement means -- which is just slightly possible -- then this function maps values 'n' to 'n' times the identity unit of R. Which is equal to the identity unit of Z, so I think that part of the definition is more-or-less covered.

How do I go about using the first two parts of the definition?

The function is just f(n) = n right?

so do I just sub in (a+b) for n?

f(a+b) = f(a) + f(b) ???

Is there anyway I can actually show that this is the case? I mean isn't this intuitive/properly defined upon the integers?

same for the other part

f(ab) = f(a)*f(b) ..... i'm just not sure how to actuallyshowthis...

thanks for any help.

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# Show that a f: Z -> R , n -> n*1(subr) is a homomorphism of rings

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