Simple locally (-1,1) nil rings
type: Item
instance of: scholarly article
title: Simple locally (-1,1) nil rings
zbMATH Open document ID: 0588.17022
DOI: 10.1016/0021-8693(86)90110-9
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: A (-1,1) ring is a right alternative ring satisfying the identity \((x,y,z)+(y,z,x)+(z,x,y)=0\), where \((x,y,z)=(xy)z-x(yz)\). A ring is called locally (-1,1) ring in case the subring generated by any two of its elements is (-1,1). This paper is devoted to the proof of the following Theorem: ''Any simple locally (-1,1) nil ring with characteristic \(\neq 2,3\) is associative.
reviewed by: Alberto Elduque
Mathematics Subject Classification ID: 17D15
Mathematics Subject Classification ID: 17D20
zbMATH DE Number: 3944107
zbMATH Keywords: associativity
zbMATH Keywords: Shirsov locally right nilpotent
zbMATH Keywords: right alternative ring
zbMATH Keywords: simple locally (-1,1) nil ring
author: Irvin Roy Hentzel
author: Harry F. Smith
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90110-9
OpenAlex ID: W1989375156
cites work: The characterization of (-1,1) rings
cites work: Alternative nil rings
cites work: Simple right alternative rings
cites work: Q5522244
cites work: Q3869506
cites work: Right alternative rings
cites work: Q3889234
description: scientific article; zbMATH DE number 3944107