Please compute;

Hom(z,q/z)=?

Hom(q,q/z)=?

and also please prove that Q is an injective Z-module.

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- Jul 1st 2011, 02:49 AMseventhsonCompute Hom(q,q/z)
Please compute;

Hom(z,q/z)=?

Hom(q,q/z)=?

and also please prove that Q is an injective Z-module. - Jul 1st 2011, 03:39 PMJose27Re: Compute Hom(q,q/z)
is trivially isomorphic to since any morphism is determined by where it sends . To prove that is injective take any morphism with then, since is divisible there exists with take with then where is the inclusion, conclude by Baer's criterion. I don't have the answer to the second but maybe the fact that is of use.

- Jul 5th 2011, 11:52 PMseventhsonRe: Compute Hom(q,q/z)
thank you jose i got it. I will try for the others.