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Proceedings of the American Mathematical Society

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

 
 

 

Nil subrings of endomorphism rings of modules


Author: Joe W. Fisher
Journal: Proc. Amer. Math. Soc. 34 (1972), 75-78
MSC: Primary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1972-0292878-2
MathSciNet review: 0292878
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Abstract: Let M be an R-module and let $ {\text{End}_R}(M)$ be the ring of all R-endomorphisms of M. If M is Artinian, then each nil subring of $ {\text{End}_R}(M)$ is nilpotent. If M is Noetherian, then the indices of nilpotency of the nil subrings of $ {\text{End}_R}(M)$ are bounded.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292878-2
Keywords: Nil ring, T-nilpotent ring, nilpotent ring, endomorphism ring, Artinian module, Noetherian module, injective Noetherian module
Article copyright: © Copyright 1972 American Mathematical Society

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