CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

A Theorem on Unit-Regular Rings

  Published:2009-12-04
 Printed: Jun 2010
  • Tsiu-Kwen Lee
  • Yiqiang Zhou
Format:   HTML   LaTeX   MathJax  

Abstract

Let $R$ be a unit-regular 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 $n\ge 0$.
Keywords: morphic rings, unit-regular rings, skew polynomial rings morphic rings, unit-regular rings, skew polynomial rings
MSC Classifications: 16E50, 16U99, 16S70, 16S35 show english descriptions von Neumann regular rings and generalizations
None of the above, but in this section
Extensions of rings by ideals
Twisted and skew group rings, crossed products
16E50 - von Neumann regular rings and generalizations
16U99 - None of the above, but in this section
16S70 - Extensions of rings by ideals
16S35 - Twisted and skew group rings, crossed products
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/