en عمومى General پژوهشي Research paper <p>A ring $R$ with identity is called ``clean&#39&#39 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&#39&#39 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 $g(x)$.</p> Clean ring, g(x)-clean ring, Weakly g(x)-clean ring. 83 91 http://ijmsi.ir/browse.php?a_code=A-10-1-116&slc_lang=en&sid=1 Nahid Ashrafi 10031947532846002219 10031947532846002219 Yes Zahra Ahmadi 10031947532846002220 10031947532846002220 No