设$\mathscr{AC}$是满足Auslander条件的左R-模类,$\mathscr{AC}$<∞表示$\mathscr{AC}$-维数有限的左R-模类.通过余倾斜模以及余倾斜余挠对的定义引出了余倾斜-相似余挠对的定义,并通过Auslander-Gorenstein环以及Auslander-regular环的概念,给出了在满足Auslander条件的Artin代数中,$\mathscr{AC}$<∞诱导出余倾斜余挠对以及余倾斜-相似余挠对的等价刻画.进而说明了Auslander和Reiten猜想的有效性:满足Auslander条件的Artin代数是Gorenstein代数.
Assuming that $\mathscr{AC}$ is the class of left R-modules satisfying the Auslander condition, and $\mathscr{AC}$<∞ represents the left R-module class with finite $\mathscr{AC}$-dimension. The definition of cotilting-like cotorsion pairs is introduced through the definitions of cotilting modules and cotilting cotorsion pairs. With the concepts of Auslander-Gorenstein rings and Auslander-regular rings, there are some equivalent characterizations of cotilting cotorsion pairs and cotilting-like cotorsion pairs induced by $\mathscr{AC}$<∞ on an Artin algebra R that satisfies the Auslander condition. This leads to some criteria for the validity of the Auslander and Reiten conjecture, which says that an Artin algebra satisfying the Auslander condition is Gorenstein.
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