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Tachikawa's second conjecture implies the Auslander-Reiten conjecture
We prove that Tachikawa's second conjecture implies the Auslander-Reiten conjecture for artin algebras over a commutative artinian ring. The proof uses the two-fold trivial extension of an algebra. Together with known implications, it follows that the Auslander-Reiten conjecture, the generalized Nak
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