| $n$-Clean Rings with Involutions |
| Received:April 12, 2015 Revised:September 18, 2015 |
| Key Words:
$*$-clean ring $n$-$*$-clean ring clean ring $n$-clean ring
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| Fund Project: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) and the Educational Foundation of Anhui Normal University (Grant No.2013qnzx35). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.02.008 |
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