On the Krull-Schmidt-Azumaya Theorem for Integral Group Rings


Authors:   Peter Hindman
           Department of Mathematics, University of Georgia,
           Athens, Georgia 30602

           Lee Klingler
           Department of Mathematical Sciences, Florida Atlantic University,
           Boca Raton, Florida 33431-0991

           Charles Odenthal
           Department of Mathematics, University of Toledo,
           Toledo, Ohio 43606-3390

Abstract:  We show that the torsion free Krull-Schmidt-Azumaya Theorem
holds for the integral group ring ZD_8, where D_8 is the dihedral group
of order 8, but torsion free cancellation (and hence also the torsion
free Krull-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
being the only open case.