An analogue for rings of a group problem of P. Erdős and B. H. Neumann
type: Item
instance of: scholarly article
title: An analogue for rings of a group problem of P. Erdős and B. H. Neumann
zbMATH Open document ID: 0905.16011
DOI: 10.1023/A:1006531605931
author: Howard E. Bell
author: Luise-Charlotte Kappe
author: A. Klein
published in: Acta Mathematica Hungarica
publication date: 1998-11-22T00:00:00Z
review text: In response to a question posed by Erdős, B. H. Neumann studied groups having no infinite subsets of pairwise non-commuting elements, which he characterized as those with center of finite index. Following Neumann's terminology, the authors define a ring \(R\) to be a Paul Erdős ring, or PE-ring, if every set of pairwise non-commuting elements is finite. They show that the center of every PE-ring is of finite index and establish several equivalent characterizations of PE-rings. They also discuss near-commutativity of PE-rings, in several different senses of near-commutativity and characterize rings with finite commutator ideal.
Mathematics Subject Classification ID: 16U70
Mathematics Subject Classification ID: 16U80
Mathematics Subject Classification ID: 20F24
zbMATH DE Number: 1225562
zbMATH Keywords: PE-rings
zbMATH Keywords: FC-groups
zbMATH Keywords: near-commutativity of rings
zbMATH Keywords: sets of noncommuting elements
zbMATH Keywords: center
MaRDI profile type: Publication
full work available at URL: a:1006531605931
OpenAlex ID: W1811872423
description: scientific article; zbMATH DE number 1225562