2-clean rings
| dc.creator | Wang, Zhou | |
| dc.creator | Chen, Jianlong | |
| dc.date | 2006-10-30 | |
| dc.date.accessioned | 2026-07-07T07:29:37Z | |
| dc.date.available | 2026-07-07T07:29:37Z | |
| dc.description | 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 ring 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 $B(R)$ of all $ω\times ω$ row and column-finite matrices over any ring $R$ is 2-clean. Finally, the group ring $RC_{n}$ is considered where $R$ is a local ring. \vskip 0.5cm {\bf Key words:}\quad 2-clean rings, 2-good rings, free modules, row and column-finite matrix rings, group rings. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610918 | |
| dc.identifier | http://arxiv.org/abs/math/0610918 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118177 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16D70, 16D40, 16S50 | |
| dc.title | 2-clean rings | |
| dc.type | text |