# Sh:693

• Shelah, S., & Trlifaj, J. (2001). Spectra of the \Gamma-invariant of uniform modules. J. Pure Appl. Algebra, 162(2-3), 367–379.
• Abstract:
For a ring R, denote by {\rm 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 {\rm 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 {\rm Spec}^R_\kappa (\Gamma) is full. We also derive some consequences for the complexity of Ziegler spectra of infinite dimensional algebras.
• published version (13p)
Bib entry
@article{Sh:693,
author = {Shelah, Saharon and Trlifaj, Jan},
title = {{Spectra of the $\Gamma$-invariant of uniform modules}},
journal = {J. Pure Appl. Algebra},
fjournal = {Journal of Pure and Applied Algebra},
volume = {162},
number = {2-3},
year = {2001},
pages = {367--379},
issn = {0022-4049},
mrnumber = {1843814},
mrclass = {16D70 (03C60 06C05 16D50)},
doi = {10.1016/S0022-4049(00)00118-3},
note = {\href{https://arxiv.org/abs/math/0009060}{arXiv: math/0009060}},
arxiv_number = {math/0009060}
}