On the Jacobson radical of some endomorphism rings

Dugas, Manfred

doi:10.1090/S0002-9939-1988-0934850-4

On the Jacobson radical of some endomorphism rings
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by Manfred Dugas

Proc. Amer. Math. Soc. 102 (1988), 823-826

DOI: https://doi.org/10.1090/S0002-9939-1988-0934850-4

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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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