Radicals of Abelian Groups
Document Type
Article
Publication Date
1990
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
The descriptions of torsion theories and of torsion valued idempotent preradicals of abclian groups are well known. The description of all radicals of abelian groups is far from known and it is the purpose of this paper to demonstrat that the description of radicals whose values are torsion groups may he as complicated as the description of all torsion groups themselves. For each nou-negative integer n, we consider singly cogenerated radicals which fit between the radicals Pw+n+1and Pw+n showing that there is a proper class of such radicals forming a chain therein. We also examine other intervals in the lattice of radicals showing either gaps or the existence of singly cogenerated radicals in these intervals.
Publication Title
Communications in Algebra
Volume
18
Issue
2
First Page
403
Last Page
411
Recommended Citation
Cutler, D. O.,
Fay, T. H.
(1990). Radicals of Abelian Groups. Communications in Algebra, 18(2), 403-411.
Available at: https://aquila.usm.edu/fac_pubs/7368