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Proceedings of the American Mathematical Society

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

 

 

Nilpotency in endomorphism rings


Author: Robert Gordon
Journal: Proc. Amer. Math. Soc. 45 (1974), 38-40
MSC: Primary 16A22
DOI: https://doi.org/10.1090/S0002-9939-1974-0346000-6
MathSciNet review: 0346000
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Abstract: Nil subrings of the endomorphism ring of a module with finite Krull dimension sequence are nilpotent. This includes the case of a module with finite Krull dimension as well as noetherian modules. The method used is to embed the endomorphism ring, modulo a nilpotent ideal, in the endomorphism ring of an artinian object of a Grothendieck category.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0346000-6
Keywords: Module with Krull dimension, Krull dimension sequence, endomorphism ring, nil ring, nilpotent ring, artinian object, Grothendieck category, noetherian module, noetherian ring, ring of quotients
Article copyright: © Copyright 1974 American Mathematical Society