ON THE KRULL-SCHMIDT-AZUMAYA THEOREM FOR INTEGRAL GROUP-RINGS

Authors
HINDMAN P KLINGLER L ODENTHAL CJ
Citation
P. Hindman et al., ON THE KRULL-SCHMIDT-AZUMAYA THEOREM FOR INTEGRAL GROUP-RINGS, Communications in algebra, 26(11), 1998, pp. 3743-3758
Citations number
12
Categorie Soggetti
Mathematics,Mathematics
Journal title
Communications in algebra → ACNP
ISSN journal
00927872
Volume
26
Issue
11
Year of publication
1998
Pages
3743 - 3758
Database
ISI
SICI code
0092-7872(1998)26:11<3743:OTKTFI>2.0.ZU;2-8
Abstract
We show that the torsion free Krull-Schmidt-Azumaya Theorem holds for the integral group ring Z D-8, where D-8 is the dihedral group of orde r 8, but torsion free cancellation land hence also the torsion free Kr ull-Schmidt-Azumaya theorem) fails for the integral group ring ZD(32). We summarize the cases for which the integral group ring ZG is known to satisfy the torsion free Krull-Schmidt-Azumaya Theorem, ZD(16) bein g the only open case.