Publications de l’Institut Mathématique, Nouvelle Série Vol. 102[116], pp. 195–202 (2017) 

Topologically boolean and $g\left(x\right)$clean ringsAngelina Yan Mui Chin, Kiat Tat QuaInstitute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia; Department of Mathematical and Actuarial Sciences, University Tunku Abdul Rahman, Kajang, Selangor, MalaysiaAbstract: Let $R$ be a ring with identity and let $g\left(x\right)$ be a polynomial in $Z\left(R\right)\left[x\right]$ where $Z\left(R\right)$ denotes the center of $R$. An element $r\in R$ is called $g\left(x\right)$clean if $r=u+s$ for some $u,s\in R$ such that $u$ is a unit and $g\left(s\right)=0$. The ring $R$ is $g\left(x\right)$clean if every element of $R$ is $g\left(x\right)$clean. We consider $g\left(x\right)=x(xc)$ where $c$ is a unit in $R$ such that every root of $g\left(x\right)$ is central in $R$. We show, via settheoretic topology, that among conditions equivalent to $R$ being $g\left(x\right)$clean, is that $R$ is right (left) $c$topologically boolean. Keywords: $g\left(x\right)$clean, $n$clean, topologically boolean Classification (MSC2000): 16U99 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 3 Nov 2017. This page was last modified: 29 Jan 2018.
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