Geodesic
2-Clean Rings
Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 145-153

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DOI

$\text{A}$ ring $R$ is said to be $n$ -clean if every element can be written as a sum of an idempotent and $n$ units. The class of these rings contains clean rings and $n$ -good rings in which each element is a sum of $n$ units. In this paper, we show that for any ring $R$ , the endomorphism ring of a free $R$ -module of rank at least 2 is 2-clean and that the ring $B\left( R \right)$ of all $\omega \,\times \,\omega$ row and column-finite matrices over any ring $R$ is 2-clean. Finally, the group ring $R{{C}_{n}}$ is considered where $R$ is a local ring.
DOI : 10.4153/CMB-2009-017-5
Mots-clés : 16D70, 16D40, 16S50, 2-clean rings, 2-good rings, free modules, row and column-finite matrix rings, group rings 
Wang, Z.; Chen, J. L. 2-Clean Rings. Canadian mathematical bulletin, Tome 52 (2009) no. 1, pp. 145-153. doi: 10.4153/CMB-2009-017-5
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     title = {2-Clean {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {145--153},
     year = {2009},
     volume = {52},
     number = {1},
     doi = {10.4153/CMB-2009-017-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-017-5/}
}
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