On the generalized hypercentralizer of a Lie ideal in a prime ring
type: Item
instance of: scholarly article
title: On the generalized hypercentralizer of a Lie ideal in a prime ring
zbMATH Open document ID: 0921.16011
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1999-09-21T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108462
review text: Let \(R\) be an associative ring with center \(Z(R)\) and let \(U\) be a noncentral Lie ideal of \(R\). For any \(x,y\in R\) set \([x,y]_1=xy-yx\), for \(n>1\) set \([x,y]_n=[[x,y]_{n-1},y]_1\), and set \(H=\{r\in R\mid[r,u^n]_m=0\) for all \(u\in U\) with \(n=n(r,u)\geq 1\) and \(m=m(r,u)\geq 1\}\). The main result in the paper proves that when \(R\) is a prime ring containing no nonzero nil right ideal then either \(H=Z(R)\) or \(R\) embeds in \(M_2(F)\) for \(F\) a field.
reviewed by: Charles Lanski
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 1279139
zbMATH Keywords: hypercentralizers
zbMATH Keywords: centralizers
zbMATH Keywords: centers
zbMATH Keywords: Lie ideals
zbMATH Keywords: prime rings
author: Vincenzo De Filippis
author: M. Onofrio Di Vincenzo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1279139