  We give a method of producing a Polish module over an arbitrary subring of
$\mathbb Q$ from an ideal of subsets of $\mathbb N$ and a sequence in $\mathbb
N$. The method allows us to construct two Polish $\mathbb Q$-vector spaces, $U$
and $V$, such that
  -- both $U$ and $V$ embed into $\mathbb R$ but
  -- $U$ does not embed into $V$ and $V$ does not embed into $U$,
  where by an embedding we understand a continuous $\mathbb Q$-linear
injection. This construction answers a question of Frisch and Shinko. In fact,
our method produces a large number of incomparable with respect to embeddings
Polish $\mathbb Q$-vector spaces.
