Strong cleanness of the $2\times 2$ matrix ring over a general local ring

Simple item page
dc.creatorYang, Xiande
dc.creatorZhou, Yiqiang
dc.date2008-05-03
dc.date.accessioned2026-07-07T09:36:54Z
dc.date.available2026-07-07T09:36:54Z
dc.descriptionA ring $R$ is called strongly clean if every element of $R$ is the sum of a unit and an idempotent that commute with each other. A recent result of Borooah, Diesl and Dorsey \cite{BDD05a} completely characterized the commutative local rings $R$ for which ${\mathbb M}_n(R)$ is strongly clean. For a general local ring $R$ and $n>1$, however, it is unknown when the matrix ring ${\mathbb M}_n(R)$ is strongly clean. Here we completely determine the local rings $R$ for which ${\mathbb M}_2(R)$ is strongly clean.
dc.description12 pages, to appear in Journal of Algebra
dc.identifierhttps://arxiv.org/abs/0805.0359
dc.identifierhttp://arxiv.org/abs/0805.0359
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160279
dc.subjectRings and Algebras
dc.titleStrong cleanness of the $2\times 2$ matrix ring over a general local ring
dc.typetext

Files

Collections

arXiv