TY - JOUR
T1 - WEAKLY g(x)-CLEAN RINGS
TT -
JF - IJMSI
JO - IJMSI
VL - 7
IS - 2
UR - http://ijmsi.ir/article-1-353-en.html
Y1 - 2012
SP - 83
EP - 91
KW - Clean ring
KW - g(x)-clean ring
KW - Weakly g(x)-clean ring.
N2 - 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 $g(x)$.
M3 10.7508/ijmsi.2012.02.008
ER -