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Spectra of Modules

✍ Scribed by Peter Jørgensen

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
240 KB
Volume
244
Category
Article
ISSN
0021-8693

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✦ Synopsis

This manuscript solves the problem that the so-called "stable category" Mod of an Artin algebra is in general not triangulated. The method is to mimick topology and hence first form the Spanier-Whitehead category Stab Mod and then construct a category Spectra of "spectra of modules" which completes the compact part of Stab Mod under small coproducts. Spectra is then a triangulated substitute for Mod .

The main results are that Spectra is a compactly generated triangulated category which contains the compact part of Stab Mod as a full subcategory and even admits a precise description of its compact objects, which only form a small set of isomorphism classes.

As an application, it is proved that over an Artin algebra, the Gorenstein projective modules form a pre-covering class. This was previously only known for rings satisfying strong homological conditions.

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Spectra of the Γ-invariant of uniform mo
Spectra of the Γ-invariant of uniform modules
✍ Saharon Shelah; Jan Trlifaj 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 140 KB

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 dire