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Kernel of a field homomorphism

  1. Apr 6, 2005 #1
    Show that the kernel of a field homomorphism is either the trivial homomorphism or isomorphic to the field.

    I've tried to see it as a factor group, but I'm stuck. Can someone help?

  2. jcsd
  3. Apr 6, 2005 #2

    matt grime

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    I'm sorry, are you think ing of kernels as morphisms or objects? Cos you refer to the kernel as a homomorphism and some thing that is isomorphic to the field.

    In any case the kernel of a ring homomorphism (of which a field homomrphism is a special case) is an ideal. So how many ideals of a field are there?
    Last edited: Apr 6, 2005
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