A note on strongly prime radicals
type: Item
instance of: scholarly article
title: A note on strongly prime radicals
zbMATH Open document ID: 0852.16015
DOI: 10.1007/BF01874618
author: J. F. Watters
published in: Acta Mathematica Hungarica
publication date: 1996-12-08T00:00:00Z
review text: The author gives certain details of his well-known example of the ring which was used by Handelman and Lawrence to show that the left and right strongly prime radicals of a ring need not coincide. The example is used to prove that the classes of right strongly prime rings, left strongly prime rings and uniformly strongly prime rings are not normal classes and that the corresponding radicals are not normal radicals. It is also proved that, in the category of rings with identity, strongly prime and uniformly strongly prime are Morita invariants, as is the semisimplicity with respect to strongly primeness.
reviewed by: Dwight M. Olson
Mathematics Subject Classification ID: 16N60
Mathematics Subject Classification ID: 16N80
zbMATH DE Number: 878097
zbMATH Keywords: strongly prime radicals
zbMATH Keywords: right strongly prime rings
zbMATH Keywords: left strongly prime rings
zbMATH Keywords: uniformly strongly prime rings
zbMATH Keywords: normal radicals
zbMATH Keywords: Morita invariants
zbMATH Keywords: semisimplicity
MaRDI profile type: Publication
cites work: Certain classes of ideals in group rings II
cites work: Strongly Prime Rings
cites work: Normal radicals
cites work: Normal radicals and normal classes of rings
cites work: Q3755592
cites work: The strongly prime radical of crossed products
cites work: ON THE GROENEWALD-HEYMAN STRONGLY PRIME RADICAL
description: scientific article; zbMATH DE number 878097