Auslander–Reiten conjecture of the tilting theorem

Let [Formula: see text] be a Noetherian algebra and [Formula: see text]-[Formula: see text] be an [Formula: see text]-tilting module with [Formula: see text]. Then [Formula: see text] satisfies Auslander–Reiten conjecture if and only if so does [Formula: see text]. As a consequence, we obtain that Auslander–Reiten conjecture is left and right symmetric for a certain Noetherian algebra.