Some ＊-Clean Group Ringst
Some ＊-Clean Group Ringst作者机构：Department of Mathematics Southeast University Nanjing 210096 China Department of Mathematics and Physics Nanjing Institute of Technology Nanjing 211167 China Department of Mathematics Brock University St. Catharines L2S 3A1 Canada
出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)
年 卷 期：2015年第22卷第1期
页 面：169-180页
核心收录：
学科分类：1004[医学-公共卫生与预防医学(可授医学、理学学位)] 07[理学] 070104[理学-应用数学] 100403[医学-营养与食品卫生学] 0701[理学-数学] 10[医学]
基 金：This research was supported in part by the National Natural Science Foundation of China (11371089 11201064) the Specialized Research Fund for the Doctoral Program of Higher Education (20120092110020) the Natural Science Foundation of Jiangsu Province (BK20130599) and a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada
主 题：group ring clean ring,*-clean ring
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.
维普期刊数据库