Strong cleanness of matrix rings over commutative rings
| dc.creator | Couchot, Francois | |
| dc.date | 2008-04-08 | |
| dc.date.accessioned | 2026-07-07T12:18:12Z | |
| dc.date.available | 2026-07-07T12:18:12Z | |
| dc.description | Let $R$ be a commutative local ring. It is proved that $R$ is Henselian if and only if each $R$-algebra which is a direct limit of module finite $R$-algebras is strongly clean. So, the matrix ring $\mathbb{M}_n(R)$ is strongly clean for each integer $n>0$ if $R$ is Henselian and we show that the converse holds if either the residue class field of $R$ is algebraically closed or $R$ is an integrally closed domain or $R$ is a valuation ring. It is also shown that each $R$-algebra which is locally a direct limit of module-finite algebras, is strongly clean if $R$ is a $π$-regular commutative ring. | |
| dc.identifier | https://arxiv.org/abs/0804.1221 | |
| dc.identifier | http://arxiv.org/abs/0804.1221 | |
| dc.identifier | Communications in Algebra 36, 2 (2008) 346-351 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/212329 | |
| dc.subject | Rings and Algebras | |
| dc.subject | MCS 13H99, 16U99 | |
| dc.title | Strong cleanness of matrix rings over commutative rings | |
| dc.type | text |