%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