On -good module categories without short cycles

Authors:
Bangming Deng and Bin Zhu

Journal:
Proc. Amer. Math. Soc. **129** (2001), 69-77

MSC (2000):
Primary 16G10, 16G60

DOI:
https://doi.org/10.1090/S0002-9939-00-05518-0

Published electronically:
June 14, 2000

MathSciNet review:
1694857

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Abstract: Let be a quasi-hereditary 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:
https://doi.org/10.1090/S0002-9939-00-05518-0

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