  For a ring R, denote by Spec^R_kappa(Gamma) the kappa-spectrum of the
Gamma-invariant of strongly uniform right R-modules. Recent realization
techniques of Goodearl and Wehrung show that Spec^R_{aleph_1}(Gamma) is full
for suitable von Neumann regular algebras R, but the techniques do not extend
to cardinals kappa>aleph_1. By a direct construction, we prove that for any
field F and any regular uncountable cardinal kappa there is an F-algebra R such
that Spec^R_kappa(Gamma) is full. We also derive some consequences for the
complexity of Ziegler spectra of infinite dimensional algebras.
