Spectra of the Gamma-invariant of uniform modules
Logic
2007-05-23 v1 Rings and Algebras
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.
Cite
@article{arxiv.math/0009060,
title = {Spectra of the Gamma-invariant of uniform modules},
author = {Saharon Shelah and Jan Trlifaj},
journal= {arXiv preprint arXiv:math/0009060},
year = {2007}
}