Ringel’s right-strongly quasi-hereditary algebras are a distinguished class of quasi-hereditary algebras of Cline–Parshall–Scott. We give characterizations of these algebras in terms of heredity chains and right rejective subcategories. We prove that any artin algebra of global dimension at most two is right-strongly quasi-hereditary. Moreover we show that the Auslander algebra of a representation-finite algebra $A$ is strongly quasi-hereditary if and only if $A$ is a Nakayama algebra.

中文翻译：

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强准遗传代数和拒绝子类别

Ringel 的右强拟遗传代数是 Cline-Parshall-Scott 的一类杰出的拟遗传代数。我们根据遗传链和右排斥子类别来描述这些代数。我们证明了任何全局维数至多为 2 的 artin 代数是右强准遗传的。此外，我们证明了表示有限代数的 Auslander 代数$澳元强准遗传当且仅当$澳元是中山代数。