We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian algebras over commutative Noetherian rings. Firstly, in the introduction, we will examine its relevance by showing that in an standard situation, the validity of this dual implies the validity of the Auslander-Reiten Conjecture itself. Moreover, in two important cases these two notions coincide: Artin algebras, and Noetherian algebras over complete local Noetherian rings. In this regard we will prove the following theorem: Let \((R, \mathfrak {m})\) be d-Gorenstein, d ≥ 2, and let Λ be a Noetherian R-algebra which is Gorenstein and (maximal) Cohen-Macaulay as R-module. If M is an Artinian self-orthogonal Gorenstein injective Λ-module such that \({\text {Hom}}_{\Lambda }({\Lambda }_{\mathfrak {p}}, M)\) is an injective \({\Lambda }_{\mathfrak {p}}\)-module for every nonmaximal prime ideal \(\mathfrak {p}\) of R, then M is injective. Some applications are discussed afterwards.

在换向Noether环上的Noether代数的情况下，我们考虑著名的Auslander-Reiten猜想的对偶概念。首先，在引言中，我们将通过显示其对偶关系的有效性进行检验，以表明在标准情况下，该对偶的有效性暗含着奥兰德-里滕猜想本身的有效性。此外，在两个重要情况下，这两个概念是重合的：Artin代数和完全局部Noether环上的Noether代数。在这方面，我们将证明以下定理：设\（（R，\ mathfrak {M}）\）被ð -Gorenstein，d ≥2，让Λ是诺特ř代数其的Gorenstein和（最大）科恩-Macaulay作为R模块。如果M是一个Artinian自正交Gorenstein内射型Λ-模，使得\（{\ text {Hom}} _ {\ Lambda}（{\ Lambda __ {\ mathfrak {p}}，M）\）是内射型\（ {\ LAMBDA} _ {\ mathfrak {p}} \） -模为每个非最大素理想\（\ mathfrak {p} \）的[R，然后中号是单射。随后讨论一些应用。