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.
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页码：539 / 544
页数：6
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