On the Krull-Schmidt-Azumaya theorem for integral group rings

被引：1

作者：

Hindman, P ^{[1
]}

Klingler, L

Odenthal, CJ

机构：

[1] Univ Georgia, Dept Math, Athens, GA 30602 USA

[2] Florida Atlantic Univ, Dept Math Sci, Boca Raton, FL 33431 USA

来源：

COMMUNICATIONS IN ALGEBRA | 1998年 / 26卷 / 11期

关键词：

Krull-Schmidt-Azumaya; unique decomposition; integral group ring;

D O I：

10.1080/00927879808826371

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 order 8, but torsion free cancellation land 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.

引用

页码：3743 / 3758

页数：16

共 12 条

[1]

CURTIS CW, 1981, METHOD REPRESENTATIO, V1

[2] FINITE-GROUPS WITH TRIVIAL CLASS GROUPS [J].