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Spectra of the Γ-invariant of uniform modules

✍ Scribed by Saharon Shelah; Jan Trlifaj

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
140 KB
Volume
162
Category
Article
ISSN
0022-4049

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✦ Synopsis

For a ring R, denote by Spec (Ä; R) the Ä-spectrum of the -invariant of strongly uniform right R-modules. Recent realization techniques of Goodearl and Wehrung show that Spec (ℵ1; R) is full for a suitable von Neumann regular algebra R, but the techniques do not extend to cardinals Ä ¿ ℵ1. By a direct construction, we prove that for any ÿeld F and any regular uncountable cardinal Ä there is an F-algebra R such that Spec (Ä; R) is full. We also derive some consequences for the -invariant of strongly dense lattices of two-sided ideals, and for the complexity of Ziegler spectra of inÿnite-dimensional algebras.

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