Abstract:We study Auslander-Reiten components of an artin algebra with bounded short cycles, namely, there exists a bound for the depths of maps appearing on short cycles of non-zero non-invertible maps between modules in the given component. First, we give a number of combinatorial characterizations of almost acyclic Auslander-Reiten components. Then, we show that an Auslander-Reiten component with bounded short cycles is closely related to the connecting component of a tilted quotient algebra. In particular, the numb… Show more
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