Conjecture on torsion-free Auslander-Reiten sequences and selfinjectivity

Let $A$ be a finite-dimensional algebra over a field. An Auslander-Reiten sequence is called $n$-torsion-free when it has the torsion-freeness property of order $n$ considered in the paper. Torsion-free Auslander-Reiten conjecture. If $A$ has $n$-torsion-free Auslander-Reiten sequences for every natural number $n$, then $A$ is self-injective. This conjecture is motivated by the results of the article and extends the relationship between torsion-free Auslander-Reiten sequences and selfinjectivity established in the preceding results. Its resolution is not supplied in the source.