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On the totally acyclic condition and the Auslander-Reiten Conjecture
We prove new cases of the Auslander-Reiten conjecture under the assumption that the base ring satisfies the totally acyclic condition $(\mathbf{tac})$. A consequence of our work is that Auslander-Reiten conjecture holds in the graded setting whenever $R$ is Gorenstein and reduced. We also give an ex
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