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Strict Radicals and Endomorphism Rings
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?
History
Publication title
Acta Mathematica HungaricaVolume
124Issue
4Pagination
371-383ISSN
0236-5294Department/School
School of Natural SciencesPublisher
SpringerPlace of publication
Van Godewijckstraat 30, Dordrecht, Netherlands, 3311 GzRights statement
The original publication is available at www.springerlink.comRepository Status
- Restricted