  In two dimensional regular local rings integrally closed ideals have a unique
factorization property and have a Cohen-Macaulay associated graded ring. In
higher dimension these properties do not hold for general integrally closed
ideals and the goal of the paper is to identify a subclass of integrally closed
ideals for which they do. We restrict our attention to 0-dimensional
homogeneous ideals in polynomial rings $R$ of arbitrary dimension and identify
a class of integrally closed ideals, the Goto-class $\G^*$, that is closed
under product and that has a suitable unique factorization property. Ideals in
$\G^*$ have a Cohen-Macaulay associated graded ring if either they are monomial
or $\dim R\leq 3$. Our approach is based on the study of the relationship
between the notions of integrally closed, contracted, full and componentwise
linear ideals.
