Let Λ be an Artin algebra with a unique non-injective indecomposable projective module. In this situation, Marczinzik conjectured that the dominant dimension of Λ agrees with its finitistic dimension. In this paper, we give a proof of a stronger statement. As a byproduct, we obtain excellent control over the finitistic dimensions of Artin algebras with two simples and positive dominant dimension, and also establish the Gorenstein symmetry conjecture for all algebras under consideration.

中文翻译：

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具有两个简单和Marczinzik猜想的Artin代数的有限维数

设Λ为具有唯一的非内射不可分解射影模块的Artin代数。在这种情况下，Marczinzik推测Λ的主导维度与其有限维度一致。在本文中，我们给出了更强有力的陈述的证据。作为副产品，我们获得了对Artin代数的有限维的极好控制，具有两个简单和正的主导维，并且还为所有考虑中的代数建立了Gorenstein对称猜想。