The rational loewy series and nilpotent ideals of endomorphism rings |
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Authors: | Jose L Gómez Pardo |
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Institution: | (1) Departamento de Matematicas, Universidad de Murcia, 30001 Murcia, Spain |
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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).
The author has been partially supported by the CAICYT. |
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