The third homework assignment is now available.
Since I have got some questions regarding the third set of problems I'll make some clarifications.
1. By the category of finite modules over Z I mean the category of Z-modules of finite cardinality. Thus in the definition of projective, we only consider short exact sequences in this category.
3. By principal module I mean a module that is generated by a single element. All such modules are isomorphic to A/J for some ideal J in a natural way.