I have two exercises which are driving me crazy.
1) Is Q finitely generated Z-module?
2) Let . Show, that , where .
I have previously proved that , where G is an Abelian group and , so it's enough to show that . And I have been given the rule . So I have to show that , , is isomorphism.
I have been able to show that this function is homomorphism and injective, but the problem here is how I can show that this function is surjective?
You´re close, in fact on it, to the definition of Z-module but not to show that the finitely generated Z-submodule S of Q cannot be the hole Q...
Read carefully what Bruno wrote you: in any Z-combination of the elements of S, how many
posible denominators can there be? How many primes are there?...