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