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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)

- Thread starter JdotAckdot
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- #1

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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

mathwonk

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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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