Year: 2014
Type: preprint
Abstract: An element $a\in R$ is very clean provided that there exists an idempotent $e\in R$ such that $ae=ea$ and either $a-e$ or $a+e$ is invertible. A ring $R$ is very clean in case every element in $R$ is very clean. We explore the necessary and sufficient conditions under which a triangular $2\times 2$ matrix ring over local rings is very clean. The very clean $2\times 2$ matrices over commutative local rings are completely determined. Applications to matrices over power series are also obtained.
Source: arXiv (Cornell University)
Authors: Chen, H., Ungor, B., Halicioglu, S.
Institutions: Hangzhou Normal University, Ankara University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1596577088