On the krull-schmidt-azumaya theorem for integral group rings

@inproceedings{Hindman1998OnTK,
  title={On the krull-schmidt-azumaya theorem for integral group rings},
  author={Peter Blake Hindman and Lee Klingler and Charles J Odenthal},
  year={1998}
}
We show that the torsion free Krull-Schmidt-Azumaya Theorem holds for the integral group ring Z D 8 Were D 8 is the group of order 8, but torsion free cancellation (and hence also the torsion free Krull-Schmidt-Azumaya theorem) fails for the integral group ring Z D 32 We summarize the cases for which the integral group ring Z G is known to satisfy the torsion free Krull-Schmidt-Azumaya Theorem, Z D 16 being the only open case. 

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