n-Clean Rings with Involutions  

作　　者：Jian CUI Xiaobin YIN 

机构地区：[1]Department of Mathematics, Anhui Normal University

出　　处：《Journal of Mathematical Research with Applications》2016年第2期194-200,共7页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11401009);the Natural Science Foundation of Anhui Province(Grant No.1408085QA01);the Key Natural Science Foundation of Anhui Educational Committee(Grant No.KJ2014A082);the Educational Foundation of Anhui Normal University(Grant No.2013qnzx35)

摘　　要：A ＊-ring is called ＊-clean if every element of the ring can be written as the sum of a projection and a unit. For an integer n ≥ 1, we call a ＊-ring R n-＊-clean if for any a ∈ R,a = p ＋ u1 ＋ ··· ＋ unwhere p is a projection and ui are units for all i. Basic properties of n-＊-clean rings are considered, and a number of illustrative examples of 2-＊-clean rings which are not ＊-clean are provided. In addition, extension properties of n-＊-clean rings are discussed.A ＊-ring is called ＊-clean if every element of the ring can be written as the sum of a projection and a unit. For an integer n ≥ 1, we call a ＊-ring R n-＊-clean if for any a ∈ R,a = p ＋ u1 ＋ ··· ＋ unwhere p is a projection and ui are units for all i. Basic properties of n-＊-clean rings are considered, and a number of illustrative examples of 2-＊-clean rings which are not ＊-clean are provided. In addition, extension properties of n-＊-clean rings are discussed.

关 键 词：＊-clean ring n-＊-clean ring clean ring n-clean ring 

分 类 号：O153.3[理学—数学]