Some *-Clean Group Ringst

• 作者: Jianlong Chen Yanyan Gao Yuanlin Li
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 卫生 CLEAN环 充分必要条件 输精管 可交换 基团 环和 群环
• 年，卷（期）: 2015,（1）
• 页码范围: 169-180
• 页数: 12页
• 分类号: O153.3
• 语种: 中文

摘要

A ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection. It is obvious that *-clean rings are clean. Vas asked whether there exists a clean ring with involution that is not *-clean. In this paper, we investigate when a group ring RG is *-clean, where * is the classical involution on RG. We obtain necessary and sufficient conditions for RG to be *-clean, where R is a commutative local ring and G is one of the groups C3,C4, S3 and Q8. As a consequence, we provide many examples of group rings which are clean but not *-clean.