Abstract view
A Theorem on UnitRegular Rings


Published:20091204
Printed: Jun 2010
TsiuKwen Lee
Yiqiang Zhou
Abstract
Let $R$ be a unitregular ring and let $\sigma $ be an endomorphism of
$R$ such that $\sigma (e)=e$ for all $e^2=e\in R$ and let $n\ge 0$. It
is proved that every element of $R[x \mathinner;\sigma]/(x^{n+1})$ is
equivalent to an element of the form $e_0+e_1x+\dots +e_nx^n$, where
the $e_i$ are orthogonal idempotents of $R$. As an application, it is
proved that $R[x \mathinner; \sigma ]/(x^{n+1})$ is left morphic for each
$n\ge 0$.