On the base radical class for associative rings

B J Gardner; Robert G McDougall

doi:10.1023/A:1022882010815

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On the base radical class for associative rings

Journal article

Peer reviewed

On the base radical class for associative rings

B J Gardner and Robert G McDougall

Acta Mathematica Hungarica, Vol.98(4), pp.263-272

2003

DOI: https://doi.org/10.1023/A:1022882010815

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Abstract

Pure Mathematics

associative rings

base radical class

The base radical class L b(X), generated by a class X was introduced in [12]. It consists of those rings whose nonzero homomorphic images have nonzero accessible subrings in X. When X is homomorphically closed, L b(X) is the lower radical class defined by X, but otherwise X may not be contained in L b(X). We prove that for a hereditary radical class L with semisimple class S(R), L b(S(R)) is the class of strongly R-semisimple rings if and only if R is supernilpotent or subidempotent. A number of further examples of radical classes of the form L b(X) are discussed.

Details

Title: On the base radical class for associative rings
Authors: B J Gardner (Author) - University of Tasmania
Robert G McDougall (Author) - Central Queensland University
Publication details: Acta Mathematica Hungarica, Vol.98(4), pp.263-272
Publisher: Akademiai Kiado Rt.
Date published: 2003
DOI: 10.1023/A:1022882010815
ISSN: 0236-5294
Organisation Unit: School of Science and Engineering - Legacy; University of the Sunshine Coast, Queensland; School of Science, Technology and Engineering
Language: English
Record Identifier: 99449114002621
Output Type: Journal article

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Collaboration types: Domestic collaboration
Web Of Science research areas: Mathematics