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Does this make sense?

  1. Oct 9, 2008 #1

    tgt

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    Suppose there exists a homomorphism f:A->B then does it make sense to have

    [tex]f_{Ker(f)}:Ker(f) \to B[/tex] ?

    why doesn't my tex show up?

    Offcourse, [tex]Im(f_{Ker(f)})=1_{B}[/tex]

    Moderator Note: Fixed LaTeX.
     
    Last edited: Oct 10, 2008
  2. jcsd
  3. Oct 9, 2008 #2

    Hootenanny

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    You need to close the tex enviroment. e.g.
    Code (Text):
    [tex]\frac{dy}{dx}[ /tex]
    (without the space in the square brackets of course)
     
    Last edited: Oct 9, 2008
  4. Oct 9, 2008 #3

    morphism

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    What are you trying to say?
     
  5. Oct 9, 2008 #4
    Are you trying to say that the elements in A that are in the kernel map into B. Well yes that's true since they all map to the zero element within B.
     
  6. Oct 10, 2008 #5

    tgt

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    Given a map, we can define a new map, mapping the kernel of the map to the range of the map.
     
  7. Oct 10, 2008 #6

    morphism

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    Yes, but what's the point?
     
  8. Oct 10, 2008 #7

    HallsofIvy

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    Yes, that makes sense. It isn't very interesting, however, since [itex]f_{Ker(f)}[/itex] is just the identity map f(x)= 1B, as you say.
     
    Last edited: Oct 12, 2008
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