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


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.


Quasi-hereditary algebra Global dimension 

Mathematics Subject Classification

Primary 16G10 Secondary 16E10 


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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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© Springer Nature Switzerland AG 2018

Authors and Affiliations

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

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