Spectra of the Gamma-invariant of uniform modules

Saharon Shelah; Jan Trlifaj

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arXiv · math/0009060

Spectra of the Gamma-invariant of uniform modules

Saharon Shelah·Jan Trlifaj

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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.

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BibTeX RIS

Saharon Shelah, Jan Trlifaj. 2000-09-06. Spectra of the Gamma-invariant of uniform modules. https://arxiv.org/abs/math/0009060

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