Cleanness of the Group Ring of an Abelian p-Group over a Commutative Ring

被引：3

作者：

Wang, Xiulan ^{[1
]}

You, Hong ^{[2
,3
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Ctr Nat Sci, Harbin 150001, Peoples R China

[3] Soochow Univ, Dept Math, Suzhou 215006, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2012年 / 19卷 / 03期

关键词：

clean rings; group rings; abelian p-groups; EXCHANGE RINGS; IDEMPOTENTS; UNIT; SUM;

D O I：

10.1142/S1005386712000405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A ring R is called clean if every element is the sum of an idempotent and a unit, while R is called uniquely clean if this representation is unique. In this article, we prove that if R is a commutative ring and G is an abelian p-group with p in J(R), then RG is clean if and only if R is clean. Moreover, when G is a locally finite group, some conditions for RG to be uniquely clean are given.

引用

页码：539 / 544

页数：6

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