Nil polynomials of prime rings
type: Item
instance of: scholarly article
title: Nil polynomials of prime rings
zbMATH Open document ID: 0876.16014
author: Chi-Tsuen Yeh
author: Chen-Lian Chuang
published in: Journal of Algebra
publication date: 1997-06-26T00:00:00Z
review text: The authors prove a neat and decisive result about polynomials with nilpotent values. Let \(R\) be a prime ring with extended centroid \(C\), and having no nonzero nil right ideal. If for \(f(x_1,x_2,\dots,x_m)\in C\{X\}\), the free algebra over \(C\) in noncommuting indeterminates, \(f(r_1,r_2,\dots,r_m)^n=0\) for all \(r_i\in R\) and \(n=n(r_1,\dots,r_m)\), then either \(f\) is an identity for \(R\), that is \(f(R^m)=0\), or \(R\cong M_k(\text{GF}(p^t))\).
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16R50
zbMATH DE Number: 1013952
zbMATH Keywords: polynomials with nilpotent values
zbMATH Keywords: prime rings
zbMATH Keywords: extended centroids
zbMATH Keywords: identities
reviewed by: Charles Lanski
MaRDI profile type: Publication
full work available at URL: jabr.1996.0394
OpenAlex ID: W2060110525
DOI: 10.1006/JABR.1996.0394
description: scientific article; zbMATH DE number 1013952