Finiteness of representation dimension
Author:
Osamu Iyama
Journal:
Proc. Amer. Math. Soc. 131 (2003), 10111014
MSC (2000):
Primary 16G10; Secondary 16E10
Published electronically:
July 17, 2002
MathSciNet review:
1948089
Fulltext PDF Free Access
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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 quasihereditary. As a conclusion, any artin algebra has a finite representation dimension.
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 O. Iyama: categories III: Auslander orders and AuslanderReiten quivers, to appear in Algebras and Representation theory.
 [I3]
 O. Iyama: A proof of Solomon's second conjecture on local zeta functions of orders, to appear in J. Algebra.
 [IT]
 K. Igusa, G. Todorov: On the finitistic global dimension conjecture, preprint.
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 H. Tachikawa: QuasiFrobenius rings and generalizations. Lecture Notes in Mathematics, Vol. 351, SpringerVerlag, BerlinNew York, 1973. MR 50:2233
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 C. C. Xi: On the representation dimension of finite dimensional algebras. J. Algebra 226 (2000), no. 1, 332346. MR 2001d:16027
 [X2]
 C. C. Xi: Representation dimension and quasihereditary algebras, to appear in Adv. Math.
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Additional Information
Osamu Iyama
Affiliation:
Department of Mathematics, Kyoto University, Kyoto, 6068502, Japan
Address at time of publication:
Department of Mathematics, Himeji Institute of Technology, Himeji, 6712201, Japan
Email:
iyama@kusm.kyotou.ac.jp, iyama@sci.himejitech.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002993902066169
PII:
S 00029939(02)066169
Received by editor(s):
August 6, 2001
Received by editor(s) in revised form:
October 29, 2001
Published electronically:
July 17, 2002
Communicated by:
Martin Lorenz
Article copyright:
© Copyright 2002
American Mathematical Society
