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Torsion Theories and Tilting Modules

Torsion Theories and Tilting Modules SVERRE O. SMAL 0 Throughout the paper A will denote an artin algebra and mod A will denote the category of finitely generated A-modules. Recently, subcategories of mod A which are the torsion free class or the torsion class of a torsion theory have attracted a lot of attention, especially because they play such an important role in the rapidly expanding theory of tilting, which is a generalization of the notion of partial Coxeter functor (see [6, 7 and 5]). In [2] the notions of covariantly, contravariantly and functorially finite subcategories were introduced. The reason why such subcategories of mod A are of interest is that they inherit so many of the properties of mod A, like existence of right and left almost split maps, existence of a preprojective partition and in certain cases existence of almost split sequences. In [3] it was determined when the torsion class of a torsion theory is functorially finite in mod A, and by duality the torsion free classes were also considered. However, the torsion free and the torsion class of one torsion theory were never considered simultaneously. In [8] Hoshino considers this when either the torsion class or the torsion free class http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Torsion Theories and Tilting Modules

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Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/16.5.518
Publisher site
See Article on Publisher Site

Abstract

SVERRE O. SMAL 0 Throughout the paper A will denote an artin algebra and mod A will denote the category of finitely generated A-modules. Recently, subcategories of mod A which are the torsion free class or the torsion class of a torsion theory have attracted a lot of attention, especially because they play such an important role in the rapidly expanding theory of tilting, which is a generalization of the notion of partial Coxeter functor (see [6, 7 and 5]). In [2] the notions of covariantly, contravariantly and functorially finite subcategories were introduced. The reason why such subcategories of mod A are of interest is that they inherit so many of the properties of mod A, like existence of right and left almost split maps, existence of a preprojective partition and in certain cases existence of almost split sequences. In [3] it was determined when the torsion class of a torsion theory is functorially finite in mod A, and by duality the torsion free classes were also considered. However, the torsion free and the torsion class of one torsion theory were never considered simultaneously. In [8] Hoshino considers this when either the torsion class or the torsion free class

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Sep 1, 1984

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