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What do you call this homomorphism?

  1. Oct 15, 2008 #1

    tgt

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    f:A->A but f(a) does not equal a for all a in A.
     
  2. jcsd
  3. Oct 15, 2008 #2
    Endomorphism?
     
  4. Oct 15, 2008 #3
    If set of all homomorphism is denoted as U,
    and identity mapping is denoted as I

    That is complementary set of identity map.
    denoted as U-I
     
  5. Oct 16, 2008 #4

    HallsofIvy

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    So you have a "set of homomorphisms" minus a single homomorphism? U- {I} would make more sense. But I would interpret "does not equal a for all a in A" as meaning f(a) is NEVER equal to a.
     
  6. Oct 16, 2008 #5
    I am confused, too.
    A group homomorphism always
    maps 1 to 1, so...
     
  7. Oct 17, 2008 #6

    tgt

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    fair point. It's probably an endomorphism.
     
  8. Oct 17, 2008 #7

    tgt

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    that seems right.
     
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