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

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

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 whic...

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Veröffentlicht in:Communications in algebra 1998-01, Vol.26 (11), p.3743-3758
Hauptverfasser: Hindman, Peter, Klingler, Lee, Odenthal, Charles J.
Format: Artikel
Sprache:eng
Schlagworte:
integral group ring
Krull-schmidt-azumaya
Primary:20C10
Secondary:16D70
unique decomposition
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Zusammenfassung: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927879808826371