The auslander-reiten translation in submodule categories
Let Lambda be an artin algebra or, more generally, a locally bounded associative algebra, and S(Lambda) the category of all embeddings (A subset of B) where B is a finitely generated Lambda-module and A is a submodule of B. Then S(Lambda) is an exact Krull-Schmidt category which has Auslander-Reiten sequences. In this manuscript we show that the Auslander-Reiten translation in S(Lambda) can be computed within mod Lambda by using our construction of minimal monomorphisms. If in addition. is uniserial, then any indecomposable nonprojective object in S(Lambda) is invariant under the sixth power of the Auslander-Reiten translation.
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AMS