关键词: Auslander条件, 余倾斜-相似余挠对, 余倾斜余挠对, Gorenstein环, 纯内射模

Abstract: 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.

Key words: Auslander condition, cotilting-like cotorsion pair, cotilting cotorsion pair, Gorenstein ring, pure-injective module