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Strict Radicals and Endomorphism Rings


Gardner, BJ, Strict Radicals and Endomorphism Rings, Acta Mathematica Hungarica, 124, (4) pp. 371-383. ISSN 0236-5294 (2009) [Refereed Article]

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DOI: doi:10.1007/s10474-009-8210-2


We consider the determination of ring radicals by classes of modules as rst discussed by Andrunakievich and Ryabukhin, but in cases where the modules concerned are dened by additive properties. Such a radical is the upper radical dened by the class of subrings of a class of endomorphism rings of abelian groups and is therefore strict. Not every strict radical is of this type, and while the A-radicals are of this type, there are others, including some special radicals. These investigations bring radical theory into contact with (at least) two questions from other parts of algebra. Which rings are endomorphism rings? For a given ring R, which abelian groups are non-trivial R-modules?

Item Details

Item Type:Refereed Article
Keywords:radical,strict radical,endomorphism ring
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Gardner, BJ (Dr Barry Gardner)
ID Code:58265
Year Published:2009
Web of Science® Times Cited:1
Deposited By:Mathematics
Deposited On:2009-09-23
Last Modified:2010-03-25
Downloads:2 View Download Statistics

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