Originally Posted by

**empyreandance** Hello friends,

I am truly stuck on this problem. Any guidance would be supremely appreciated.

Let F=Sum over x in X of **Z**x be a free **Z**-module with an infinite basis X. Then {f_x : x in X} does not form a basis of F*.

Relevant notes:

f_x is a map F -> Z given by f_x(y) = d_xy, where d is the Kronecker delta

Hints given: F* is isomorphic to the direct product over x in X **Z**x, but under this isomorphism, f_y -> {d_xy * x}, which is in the direct product over x in X of **Z**x.