%0 Journal Article %A Ashrafi, Nahid %A Ahmadi, Zahra %T WEAKLY g(x)-CLEAN RINGS %J Iranian Journal of Mathematical Sciences and Informatics %V 7 %N 2 %U http://ijmsi.ir/article-1-353-en.html %R 10.7508/ijmsi.2012.02.008 %D 2012 %K Clean ring, g(x)-clean ring, Weakly g(x)-clean ring., %X A ring $R$ with identity is called ``clean'' if $~$for every element $ain R$, there exist an idempotent $e$ and a unit $u$ in $R$ such that $a=u+e$. Let $C(R)$ denote the center of a ring $R$ and $g(x)$ be a polynomial in $C(R)[x]$. An element $rin R$ is called ``g(x)-clean'' if $r=u+s$ where $g(s)=0$ and $u$ is a unit of $R$ and, $R$ is $g(x)$-clean if every element is $g(x)$-clean. In this paper we define a ring to be weakly $g(x)$-clean if each element of $R$ can be written as either the sum or difference of a unit and a root of $g(x)$. %> http://ijmsi.ir/article-1-353-en.pdf %P 83-91 %& 83 %! %9 Research paper %L A-10-1-116 %+ %G eng %@ 1735-4463 %[ 2012