  Let $b$ be a fractional ideal of a one-dimensional Cohen-Macaulay local ring
$O$ containing a perfect field $k$. This paper is devoted to the study some
$O$-modules associated with $b$. In addition, different motivic Poincar\'e
series are introduced by considering ideal filtrations associated with $b$; the
corresponding functional equations of these Poincar\'e series are also
described.
