On stable equivalences induced by exact functors

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Let A A and B B be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence α \alpha between A A and B B such that α \alpha is induced by exact functors. We present a nice correspondence between indecomposable modules over A A and B B . As a consequence, we have the following: (1) If A A is a self-injective algebra, then so is B B ; (2) If A A and B B are finite dimensional algebras over an algebraically closed field k k , and if A A is of finite representation type such that the Auslander-Reiten quiver of A A has no oriented cycles, then A A and B B are Morita equivalent.