On the Jacobson radical of some endomorphism rings-Reference-Cited by-同舟云学术

On the Jacobson radical of some endomorphism rings

Published:1988 Issue:4 Volume:102 Page:823-826
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Dugas Manfred

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 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1988-102-04/S0002-9939-1988-0934850-4/S0002-9939-1988-0934850-4.pdf

Reference10 articles.

1. On endomorphism rings of primary abelian groups;Corner, A. L. S.;Quart. J. Math. Oxford Ser. (2),1969

2. Prescribing endomorphism algebras, a unified treatment;Corner, A. L. S.;Proc. London Math. Soc. (3),1985

3. On endomorphism rings of primary abelian groups;Dugas, Manfred;Math. Ann.,1982

4. \bysame, Almost ∑-cycle abelian 𝑝-groups, Proc. Udine Conf. on Abelian Groups and Modules, Springer-Verlag, Wien and New York, 1984, pp. 87-106.

5. Pure and Applied Mathematics, Vol. 36;Fuchs, László,1970

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