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The rational loewy series and nilpotent ideals of endomorphism rings

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Abstract

Sufficient conditions are given, in module-theoretic terms, for the idealN(S) of the endomorphism ringS of a moduleM consisting of the endomorphisms with essential kernel to be nilpotent. This extends in a natural way several known results on the nilpotency ofN(S). WhenM is a quasi-injective module such thatS is right noetherian, it is shown thatS is right artinian if and only ifM has a finite rational Loewy series whose length is, in this case, equal to the index of nilpotency ofN(S).

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Authors and Affiliations

  1. Departamento de Matematicas, Universidad de Murcia, 30001, Murcia, Spain

    Jose L. Gómez Pardo

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  1. Jose L. Gómez Pardo
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The author has been partially supported by the CAICYT.

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Gómez Pardo, J.L. The rational loewy series and nilpotent ideals of endomorphism rings. Israel J. Math. 60, 315–332 (1987). https://doi.org/10.1007/BF02780396

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  • DOI: https://doi.org/10.1007/BF02780396

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