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Finiteness of representation dimension

Author(s): Osamu Iyama
Journal: Proc. Amer. Math. Soc. 131 (2003), 1011-1014.
MSC (2000): Primary 16G10; Secondary 16E10
Posted: July 17, 2002
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Abstract: We will show that any module over an artin algebra is a direct summand of some module whose endomorphism ring is quasi-hereditary. As a conclusion, any artin algebra has a finite representation dimension.

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[I1]
O. Iyama: $\tau$-categories II: Nakayama pairs and rejective subcategories, to appear in Algebras and Representation theory.

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O. Iyama: $\tau$-categories III: Auslander orders and Auslander-Reiten quivers, to appear in Algebras and Representation theory.

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C. C. Xi: Representation dimension and quasi-hereditary algebras, to appear in Adv. Math.

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Additional Information:

Osamu Iyama
Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan
Address at time of publication: Department of Mathematics, Himeji Institute of Technology, Himeji, 671-2201, Japan
Email: iyama@kusm.kyoto-u.ac.jp, iyama@sci.himeji-tech.ac.jp

DOI: 10.1090/S0002-9939-02-06616-9
PII: S 0002-9939(02)06616-9
Received by editor(s): August 6, 2001
Received by editor(s) in revised form: October 29, 2001
Posted: July 17, 2002
Communicated by: Martin Lorenz
Copyright of article: Copyright 2002, American Mathematical Society

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