Strongly Clean Matrix Rings Over Commutative Rings
| dc.creator | Fan, Lingling | |
| dc.creator | Yang, Xiande | |
| dc.date | 2008-03-14 | |
| dc.date | 2008-08-20 | |
| dc.date.accessioned | 2026-07-07T09:57:13Z | |
| dc.date.available | 2026-07-07T09:57:13Z | |
| dc.description | A ring $R$ is called strongly clean if every element of $R$ is the sum of a unit and an idempotent that commute. By {\rm SRC} factorization, Borooah, Diesl, and Dorsey \cite{BDD051} completely determined when ${\mathbb M}_n(R)$ over a commutative local ring $R$ is strongly clean. We generalize the notion of {\rm SRC} factorization to commutative rings, prove that commutative $n$-{\rm SRC} rings $(n\ge 2)$ are precisely the commutative local rings over which ${\mathbb M}_n(R)$ is strongly clean, and characterize strong cleanness of matrices over commutative projective-free rings having {\rm ULP}. The strongly $π$-regular property (hence, strongly clean property) of ${\mathbb M}_n(C(X,{\mathbb C}))$ with $X$ a {\rm P}-space relative to ${\mathbb C}$ is also obtained where $C(X,{\mathbb C})$ is the ring of complex valued continuous functions. | |
| dc.identifier | https://arxiv.org/abs/0803.2176 | |
| dc.identifier | http://arxiv.org/abs/0803.2176 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167262 | |
| dc.subject | Rings and Algebras | |
| dc.title | Strongly Clean Matrix Rings Over Commutative Rings | |
| dc.type | text |