Is it because the coproducts and summands can be switched? Like on Rotman advanced algebra pg 431
Well, that is true in some sense, by why does that help us? What we really want to show is that each of the three Homs , , and can be reduced. How can we reduce each of these?
Right. But what is it isomorphic to? I think you need to play around with some examples before you tackle this problem man, or your just going to be taking what I say as true--you need to see it for yourself.
Hom_z(Z_5,Z_7) is isomorphic to Z_7. I am still not sure why the last three summans can be reduced. Can it be since there is an isomorphism from the from Hom(diret product of M_p) to direct sum (M_p,R^m)
Hom_z(Z_5,Z_7) is isomorphic to Z_7. I am still not sure why the last three summans can be reduced. Can it be since there is an isomorphism from the from Hom(diret product of M_p) to direct sum (M_p,R^m)
. Do you see why this is now true? Think about torsion, etc. etc. See if you can then use this to see why our problem is reuced?