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Module Homomorphisms

  1. Apr 7, 2005 #1
    If you can help, that would be great.

    Let R be a commutative ring, and A,B,M be R-modules. Prove:

    a) HomR(A x B, M) is isomorphic to HomR(A, M) x HomR(B, M)
    b) HomR(M, A x B) is isomorphic to HomR(M, A) x HomR(M, B)
     
  2. jcsd
  3. Apr 7, 2005 #2

    mathwonk

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    step one: try to write down a map from one to the other.

    e.g. given a pair of homomorphisms f:M-->A and g:M-->B. how would you construct, in the simplest most natural way, a homomorphism M-->AxB?

    conversely, given a homomorphism M-->AxB, how would you construct homomorphisms M-->A and M-->B?
     
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