Spectra of the Gamma-invariant of uniform modules

Abstract

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.