Abstract
Let M be a finitely generated module over an Artin algebra A. The Auslander–Reiten conjecture says that if \({{\rm Ext}^n_A(M, M \oplus A) = 0}\) for all natural numbers n, then M is projective. In the paper, we prove that the conjecture is true for all symmetric special biserial algebras and that it is also true for special biserial algebras with radical cube zero.
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xu, D. Auslander–Reiten conjecture and special biserial algebras. Arch. Math. 105, 13–22 (2015). https://doi.org/10.1007/s00013-015-0776-z
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DOI: https://doi.org/10.1007/s00013-015-0776-z