## Recollements of abelian categories and ideals in heredity chains—a recursive approach to quasi-hereditary algebras

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- by Nan Gao, Steffen Koenig and Chrysostomos Psaroudakis PDF
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**147**(2019), 4625-4637 Request permission

## Abstract:

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel’s characterisation of idempotent ideals occurring in heredity chains, which in turn characterises quasi-hereditary algebras recursively. Further applications are given to hereditary algebras and to Morita context rings.## References

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## Additional Information

**Nan Gao**- Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444, People’s Republic of China
- MR Author ID: 833788
- Email: nangao@shu.edu.cn
**Steffen Koenig**- Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- MR Author ID: 263193
- Email: skoenig@mathematik.uni-stuttgart.de
**Chrysostomos Psaroudakis**- Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Address at time of publication: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece
- MR Author ID: 1041820
- Email: chpsaroud@math.auth.gr
- Received by editor(s): April 25, 2018
- Received by editor(s) in revised form: February 10, 2019
- Published electronically: July 1, 2019
- Additional Notes: The first named author was supported by the National Natural Science Foundation of China (grant No. 11771272)

The third named author was supported by Deutsche Forschungsgemeinschaft (DFG, grant KO $1281/14-1$) - Communicated by: Jerzy Weyman
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 4625-4637 - MSC (2010): Primary 16G10; Secondary 17B10, 16E60, 18G15
- DOI: https://doi.org/10.1090/proc/14620
- MathSciNet review: 4011500