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Archiv der Mathematik

, Volume 112, Issue 1, pp 41–51 | Cite as

On an upper bound for the global dimension of Auslander–Dlab–Ringel algebras

  • Mayu TsukamotoEmail author
Article
  • 28 Downloads

Abstract

Lin and Xi introduced Auslander–Dlab–Ringel (ADR) algebras of semilocal modules as a generalization of original ADR algebras and showed that they are quasi-hereditary. In this paper, we prove that such algebras are always left-strongly quasi-hereditary. As an application, we give a better upper bound for the global dimension of ADR algebras of semilocal modules. Moreover, we describe characterizations of original ADR algebras to be strongly quasi-hereditary.

Keywords

Quasi-hereditary algebra Global dimension 

Mathematics Subject Classification

Primary 16G10 Secondary 16E10 

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Notes

Acknowledgements

The author wishes to express her sincere gratitude to Takahide Adachi and Professor Osamu Iyama. The author thanks Teresa Conde and Aaron Chan for informing her about the reference [17, Proposition 2], which greatly shortens her original proof.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceOsaka City UniversityOsakaJapan

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