# Sh:693

- Shelah, S., & Trlifaj, J. (2001).
*Spectra of the \Gamma-invariant of uniform modules*. J. Pure Appl. Algebra,**162**(2-3), 367–379. arXiv: math/0009060 DOI: 10.1016/S0022-4049(00)00118-3 MR: 1843814 -
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} }