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Quasi-Tilting Modules and Counter Equivalences

✍ Scribed by Riccardo Colpi; Gabriella D'Este; Alberto Tonolo

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 447 KB
Volume: 191
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1997.6873

No coin nor oath required. For personal study only.

✦ Synopsis

Given two rings R and S, we study the category equivalences T T ¡ Y Y, where T T is a torsion class of R-modules and Y Y is a torsion-free class of S-modules. These Ž . equivalences correspond to quasi-tilting triples R, V, S , where V is a bimodule R S which has, ''locally,'' a tilting behavior. Comparing this setting with tilting bimodules and, more generally, with the torsion theory counter equivalences introduced by Colby and Fuller, we prove a local version of the Tilting Theorem for quasi-tilting triples. A whole section is devoted to examples in case of algebras over a field.

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