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

TL;DR

This paper establishes that Auslander--Dlab--Ringel (ADR) algebras of semilocal modules are always left-strongly quasi-hereditary and provides improved upper bounds for their global dimension, enhancing understanding of their homological properties.

Contribution

It proves that ADR algebras are always left-strongly quasi-hereditary and offers a tighter upper bound for their global dimension, extending previous results.

Findings

ADR algebras are left-strongly quasi-hereditary

Improved upper bounds for global dimension of ADR algebras

Characterizations of when ADR algebras are strongly quasi-hereditary

Abstract

Lin and Xi introduced Auslander--Dlab--Ringel (ADR) algebras of seimlocal 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 global dimension of ADR algebras of semilocal modules. Moreover we describe characterizations of original ADR algebras to be strongly quasi-hereditary.