TITLE: Infinite direct product of the integers not a free module over the integers
QUESTION [11 upvotes]: Possible Duplicate:
Is it true that, as Z-modules, the polynomial ring and the power series ring over integers are dual to each other? 

Is there an easy proof? I only found citations but have no access. By the way: If we cross over to the rationals every vector space is free (using Zorn's lemma). But can one construct a basis of "Countable infinite product of the rationals"?

REPLY [2 votes]: See Example 3.5 at http://www.math.uconn.edu/~kconrad/blurbs/linmultialg/dualmod.pdf for an argument.