Homomorphism proof help

  • #1
(A) f: Z -> Z with a function defined as f(x)=-x

1.) f(0)=0
2.) f(a)-f(b)=-a+b=-a+b=f(a-b)
3.) -f(a)=a=a=f(-a)

Conclusion: a homomorphism

(B) f: Z2 -> Z2 with a function defined as f(x)=-x
This one I'm not sure, I doubt it is a homomorphism though.

f: g -> g
 
Last edited:

Answers and Replies

  • #2
Dick
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Z_s? s equal what? s=2 certainly is a homomorphism. s>2 may cause problems. But not with f(0).
 
  • #3


Sorry, I didn't even realize all the things i left off. But anyway, are my three proofs correct?
 
  • #4
Dick
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What three proofs? I thought there were maximum two problems here. f(x)=-x for i) Z->Z and ii) Z_2->Z_s. Whatever s is. Homomorphism, yes or no. You are being super unclear.
 
  • #5


Wow, sorry. I just transposed everything from my notes quickly. The S was suppose to be a 2, which I fixed. I also only did put up two proofs just to see if Z -> Z and Z2 -> Z2 were homomorphisms. I arrived at the same conclusion for both. I actually didn't type out the third one, I'm not sure why.
 

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