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Functorial radicals and non-abelian torsion

Published online by Cambridge University Press:  20 January 2009

Shalom Feigelstock  and
Aaron Klein
Aaron Klein
Affiliation:
Bar-Ilan UniversityRamat-Gan, Israel
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Radicals appear in many algebraic contents. For modules over a ring, they give rise to pre-torsion and torsion theories, Goldman (5), Lambek (14). In the category of groups, Kurosh, Plotkin and others have introduced radicals (6), (13), (21), but unlike the radicals in module theory these radicals are not necessarily functorial, as for example the nil radical and the Hirsch-Plotkin radical (6). The functorial method in module theory has been extended to abelian categories, Dickson (2), to the category of nilpotent groups, Hilton (8), Warfield (25), and to the category of groups, Plotkin (22), and to general categories, Wiegandt (26), Holcombe and Walker (10).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 3 , October 1980 , pp. 317 - 329
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

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