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Homework Help: Homomorphism proof help

  1. Feb 26, 2009 #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: Feb 26, 2009
  2. jcsd
  3. Feb 26, 2009 #2

    Dick

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    Re: homomorphism

    Z_s? s equal what? s=2 certainly is a homomorphism. s>2 may cause problems. But not with f(0).
     
  4. Feb 26, 2009 #3
    Re: homomorphism

    Sorry, I didn't even realize all the things i left off. But anyway, are my three proofs correct?
     
  5. Feb 26, 2009 #4

    Dick

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    Re: homomorphism

    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.
     
  6. Feb 26, 2009 #5
    Re: homomorphism

    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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