On good module categories without short cycles
Authors:
Bangming Deng and Bin Zhu
Journal:
Proc. Amer. Math. Soc. 129 (2001), 6977
MSC (2000):
Primary 16G10, 16G60
Published electronically:
June 14, 2000
MathSciNet review:
1694857
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Abstract: Let be a quasihereditary algebra, and the good module category consisting of modules which have a filtration by standard modules. An indecomposable module in is said to be on a short cycle in if there exist an indecomposable module in and a chain of two nonzero noninvertible maps . It is shown that two indecomposable modules in are isomorphic if they are not on short cycles in and have the same composition factors. Moreover, if there is no short cycle in , we show that is finite, that is, there are only finitely many isomorphism classes of indecomposables in . This is an analogue to a result in a complete module category proved by Happel and Liu.
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Additional Information
Bangming Deng
Affiliation:
Department of Mathematics, Beijing Normal University, 100875 Beijing, People’s Republic of China
Email:
dengbm@bnu.edu.cn
Bin Zhu
Affiliation:
Department of Mathematics, Beijing Normal University, 100875 Beijing, People’s Republic of China
Address at time of publication:
Department of Mathematics, Tsinghua University, 100084 Beijing, People’s Republic of China
Email:
bzhu@math.tsinghua.edu.cn
DOI:
http://dx.doi.org/10.1090/S0002993900055180
PII:
S 00029939(00)055180
Received by editor(s):
September 21, 1998
Received by editor(s) in revised form:
March 31, 1999
Published electronically:
June 14, 2000
Dedicated:
To our teacher Shaoxue Liu on the occasion of his 70th birthday
Communicated by:
Ken Goodearl
Article copyright:
© Copyright 2000
American Mathematical Society
