Hi once again! I have two questions:

a) Let a PID and a finitely generated -module. Show that the -module is free and has finite rank.

b) We have an exact sequence of modules over a PID . Show that is a free -module of rank n-m ( denoting the submodule of torsionelements).

To solve a) i tried to create an exact sequence involving Hom(M,R) but i got stuck. And for b) i do not have any ideas. Can anyone please help me?