CCR-rings
type: Item
instance of: scholarly article
title: CCR-rings
zbMATH Open document ID: 0674.16012
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: A ring is called \(\pi\)-regular (strongly regular, resp.) if for every a there exists an element x and an integer n such that \(a^ nxa^ n=a^ n\) \((a^ 2x=a\), resp.). It is CCR if every primitive homomorphic image is simple with a minimal one-sided ideal. The main result claims that in a \(\pi\)-regular semisimple CCR-ring R there exists a nonzero idempotent e such that eRe is strongly regular. It is noticed that a ring is strongly regular if and only if it is von Neumann regular and has no nonzero nilpotent elements.
reviewed by: Jaroslav Zemánek
Mathematics Subject Classification ID: 16E50
Mathematics Subject Classification ID: 16U99
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 4103291
zbMATH Keywords: minimal one-sided ideal
zbMATH Keywords: \(\pi \) -regular semisimple CCR-ring
zbMATH Keywords: nonzero idempotent
zbMATH Keywords: strongly regular
zbMATH Keywords: von Neumann regular
zbMATH Keywords: nilpotent elements
MaRDI profile type: Publication
full work available at URL: pjm.1989.137.155
OpenAlex ID: W1498505655
DOI: 10.2140/PJM.1989.137.155
author: Irving Kaplansky
description: scientific article; zbMATH DE number 4103291