Spectra of the $\Gamma$-invariant of uniform modules

by Shelah and Trlifaj. [ShTl:693]
J Pure and Applied Algebra, 2001
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.


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