  Given an homogeneous polynomial on a Banach space $E$ belonging to some
maximal or minimal polynomial ideal, we consider its iterated extension to an
ultrapower of $E$ and prove that this extension remains in the ideal and has
the same ideal norm. As a consequence, we show that the Aron-Berner extension
is a well defined isometry for any maximal or minimal ideal of homogeneous
polynomials. This allow us to obtain symmetric versions of some basic results
of the metric theory of tensor products.
