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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the Jacobson radical of some endomorphism rings


Author: Manfred Dugas
Journal: Proc. Amer. Math. Soc. 102 (1988), 823-826
MSC: Primary 20K30; Secondary 16A21, 16A65, 20K10
DOI: https://doi.org/10.1090/S0002-9939-1988-0934850-4
MathSciNet review: 934850
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Abstract: In this note we deal with a question raised by R. S. Pierce in 1963: Determine the elements of the Jacobson radical of the endomorphism ring of a primary abelian group by their action on the group. We concentrate on separable abelian $ p$-groups and give a counterexample to a conjecture of A. D. Sands. We also show that the radical can be pinned down if the endomorphism ring is a split-extension of its ideal of all small maps.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0934850-4
Keywords: Abelian $ p$-group, endomorphism ring, small endomorphisms, Jacobson radical, height-preserving maps
Article copyright: © Copyright 1988 American Mathematical Society