On strongly $g(x)$-clean rings

Details On strongly $g(x)$-clean rings On strongly $g(x)$-clean rings

2008-03-24

arxiv.org/abs/0803.3353v1

Mathematics

Rings and Algebras

8 pages

Scientific paper

Let $R$ be an associative ring with identity, $C(R)$ denote the center of $R$, and $g(x)$ be a polynomial in the polynomial ring $C(R)[x]$. $R$ is called strongly $g(x)$-clean if every element $r \in R$ can be written as $r=s+u$ with $g(s)=0$, $u$ a unit of $R$, and $su=us$. The relation between strongly $g(x)$-clean rings and strongly clean rings is determined, some general properties of strongly $g(x)$-clean rings are given, and strongly $g(x)$-clean rings generated by units are discussed.

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