AI 中文总结
本文对Auslander-Gorenstein有限维代数给出新刻画，证实Marczinzik的猜想，还新证明具有Auslander-Gorenstein关联代数的有限格必为分配格。
AI 中文摘要
我们对Auslander-Gorenstein有限维代数给出了一种新刻画，证明其恰好是具有良定义Auslander-Reiten双射的有限维代数，这证实了Marczinzik的一个猜想；我们利用该结果新证明：具有Auslander-Gorenstein关联代数的有限格必为分配格。
英文摘要
We give a new characterisation of Auslander-Gorenstein finite dimensional algebras by showing that they are exactly the finite dimensional algebras with a well-defined Auslander-Reiten bijection. This proves a conjecture of Marczinzik. We use this to give a new proof that a finite lattice with an Auslander-Gorenstein incidence algebra has to be distributive.
CommentsAddes two applications. In particular, we answer a question due to Iyama
