  We characterize the first Alexander Z[Z]-modules of ribbon surface-links in
the 4-sphere fixing the number of components and the total genus, and then the
first Alexander Z[Z]-modules of surface-links in the 4-sphere fixing the number
of components. Using the result of ribbon torus-links, we also characterize the
first Alexander Z[Z]-modules of virtual links fixing the number of components.
For a general surface-link, an estimate of the total genus is given in terms of
the first Alexander Z[Z]-module. We show a graded structure on the first
Alexander Z[Z]-modules of all surface-links and then a graded structure on the
first Alexander Z[Z]-modules of classical links, surface-links and
higher-dimensional manifold-links.
