On the structure of complete \(\nu\)-normal primitive rings and its applications
type: Item
instance of: scholarly article
title: On the structure of complete \(\nu\)-normal primitive rings and its applications
zbMATH Open document ID: 0661.16004
DOI: 10.1016/0021-8693(88)90181-0
author: Xu Yonghua
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: A structure theorem for primitive rings with non-zero socles was established by N. Jacobson. In this paper, the notions of normal primitivity and simplicity for rings are generalized to \(\nu\)-normal primitivity and \(\nu\)-simplicity. The structure of these rings is thoroughly investigated and the well-known Utumi-Faith theorem is therefore extended to infinite matrix form. Also, Goldie prime rings with right Goldie dimension are extended to the infinite case. Information for complete rings of continuous linear transformations in a vector space over a division ring is provided. Primitive rings with \(\aleph_{\nu}\)- fold transitivity are studied.
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16P60
zbMATH DE Number: 4079653
zbMATH Keywords: primitive rings with non-zero socles
zbMATH Keywords: \(\nu\)-normal primitivity
zbMATH Keywords: \(\nu\)- simplicity
zbMATH Keywords: Utumi-Faith theorem
zbMATH Keywords: Goldie prime rings
zbMATH Keywords: right Goldie dimension
zbMATH Keywords: complete rings of continuous linear transformations
reviewed by: K. P. Shum
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90181-0
OpenAlex ID: W2046473126
cites work: Q4339908
cites work: Q5519166
cites work: Q4740694
cites work: Q3919833
cites work: On the structure of primitive rings
description: scientific article; zbMATH DE number 4079653