  Let $R$ be a local Gorenstein ring with infinite residue field of arbitrary
characteristic. Let $I$ be an $R$--ideal with $g=\height I >0$, analytic spread
$\ell$, and let $J$ be a minimal reduction of $I$. We further assume that $I$
satisfies $G_{\ell}$ and ${\depth}
  R/I^j \geq \dim R/I -j+1$ for $1 \leq j \leq \ell-g$. The question we are
interested in is whether $\core{I}=J^{n+1}:\ds \sum_{b \in I} (J,b)^n$ for $n
\gg 0$. In the case of analytic spread one Polini and Ulrich show that this is
true with even weaker assumptions (\cite[Theorem 3.4]{PU}). We give a negative
answer to this question for higher analytic spreads and suggest a formula for
the core of such ideals.
