Iranian Journal of Mathematical Sciences and Informatics مجله علوم ریاضی و انفورماتیک IJMSI Basic Sciences http://ijmsi.ir 1 admin 1735-4463 2008-9473 8 10.52547/ijmsi 14 8888 13 en jalali 1391 8 1 gregorian 2012 11 1 7 2 online 1 fulltext
en WEAKLY g(x)-CLEAN RINGS 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