Volume 7, Issue 2 (11-2012)                   IJMSI 2012, 7(2): 83-91 | Back to browse issues page


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Ashrafi N, Ahmadi Z. WEAKLY g(x)-CLEAN RINGS. IJMSI. 2012; 7 (2) :83-91
URL: http://ijmsi.ir/article-1-353-en.html
Abstract:  

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 $g(x)$.

Type of Study: Research paper | Subject: General

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