| 具有对合运算的$n$-clean环 |
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| 引用本文： | 崔建,殷晓斌.具有对合运算的$n$-clean环[J].数学研究及应用,2016,36(2):194-200. |
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| 作者姓名： | 崔建 殷晓斌 |
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| 作者单位： | 安徽师范大学数学系, 安徽 芜湖 241003,安徽师范大学数学系, 安徽 芜湖 241003 |
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| 基金项目： | 国家自然科学基金(Grant No.11401009),安徽省自然科学基金(Grant No.1408085QA01),安徽高校省级自然科学研究重点项目(Grant No.KJ2014A082),安徽师范大学教育基金会(Grant No.2013qnzx35). |
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| 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.
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| 关 键 词： | $*$-clean环 $n$-$*$-clean环 clean环 $n$-clean环 |
| 收稿时间： | 2015/4/12 0:00:00 |
| 修稿时间： | 2015/9/18 0:00:00 |
$n$-Clean Rings with Involutions |
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| Jian CUI and Xiaobin YIN.$n$-Clean Rings with Involutions[J].Journal of Mathematical Research with Applications,2016,36(2):194-200. |
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| Authors: | Jian CUI and Xiaobin YIN |
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| Institution: | Department of Mathematics, Anhui Normal University, Anhui 241003, P. R. China and Department of Mathematics, Anhui Normal University, Anhui 241003, P. R. China |
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| Abstract: | 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 $n\geq 1,$ we call a $*$-ring $R$ $n$-$*$-clean if for any $a\in R,$ $a=p+u_1+\cdots+u_n$ where $p$ is a projection and $u_i$ 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. |
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| Keywords: | $*$-clean ring $n$-$*$-clean ring clean ring $n$-clean ring |
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