Abstract
Since it was shown by Baer and Kaplansky that any isomorphism of the endomorphism rings of primary abelian groups is induced by an isomorphism of the groups attention has been given to the study of these rings. Pierce raised the question of describing the radical of an endomorphism ring in terms of its action on the group and solved this problem in the torsion-complete case. Liebert2 has solved this problem for direct sums of cyclic groups; Hausen3 has solved it for totally projective groups; Hausen and Johnson4 have solved it for sufficiently projective groups.
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References
Pierce, R.S., Holomomorphisms of primary abelian groups, in Topics in Abelian Groups, Irwin, J.M. and Walker, E.A., Eds., Scott, Foresman and Co., Chicago, 1963.
Liebert, W., The Jacobson radical of some endomorphism rings, J. Reine Angew. Math., 262, 166, 1973.
Hausen, J., Quasi-regular ideals of some endomorphism rings, Ill. J. Math., 22, 845, 1977.
Hausen, J. and Johnson, J.A., Ideals and radicals of some endomorphism rings, Pacific J. Math., 22, 845, 1977.
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© 1984 Springer-Verlag Wien
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Sands, A.D. (1984). On the Radical of the Endomorphism Ring of a Primary Abelian Group. In: Göbel, R., Metelli, C., Orsatti, A., Salce, L. (eds) Abelian Groups and Modules. International Centre for Mechanical Sciences, vol 287. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2814-5_22
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DOI: https://doi.org/10.1007/978-3-7091-2814-5_22
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81847-3
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