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How does one compute the number of ring homomorphisms

  1. Jan 23, 2006 #1
    How does one compute the number of ring homomorphisms from [tex]\mathbb{Z}_2^n[/tex] to [tex]\mathbb{Z}_2^m[/tex]? Or, likewise, the number of linear mappings on those two vector spaces?
     
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  3. Jan 24, 2006 #2

    matt grime

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    By doing it. Pick a basis in one and work it out by hand. As vector spaces it's very easy, since it is just a finite set of matrices.
     
  4. Jan 24, 2006 #3
    When asked the number of linear transformations between two vector spaces V and W, is it the same as asking the number of group homomoprhisms between V and W, of which are homogeneous? Is a group homomorphism automatically honogeneous (preserves scalar multiplication)?
     
  5. Jan 24, 2006 #4

    mathwonk

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    make a conjecture and try to prove it.
     
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