On Clean Group Rings

被引：17
作者：
Zhou, Yiqiang [1 ]
机构：
[1] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada
来源：
ADVANCES IN RING THEORY | 2010年
关键词：
Clean ring; group ring; uniquely clean ring; EXCHANGE RINGS; REGULAR-RINGS; UNIT; IDEMPOTENTS; SUM;
D O I：
10.1007/978-3-0346-0286-0_22
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A ring with unity is called clean (uniquely clean) if each of its elements is (uniquely) the SUM of an idempotent and a unit. When is a group ring clean? The question seems to be difficult in general. For example, it is even unknown when the group ring of a cyclic group of order 2 is clean. After reviewing the known results, we present several new partial answers to the question. We also give a different proof of the main result on uniquely clean group rings obtained by Chen, Nicholson and Zhou [6].
引用
收藏
页码：335 / 345
页数：11
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