  An integral domain $D$ is called an SP-domain if every ideal is a product of
radical ideals. Such domains are always almost Dedekind domains, but not every
almost Dedekind domain is an SP-domain. The SP-rank of $D$ provides a natural
measure of the deviation of $D$ from being an SP-domain. In the present paper
we show that every ordinal number $\alpha$ can be realized as the SP-rank of an
almost Dedekind domain.
