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Proceedings of the American Mathematical Society

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

 

 

The endomorphism ring of an Artinian module whose homogeneous length is finite


Author: Rainer Schulz
Journal: Proc. Amer. Math. Soc. 86 (1982), 209-210
MSC: Primary 16A65; Secondary 16A22
DOI: https://doi.org/10.1090/S0002-9939-1982-0667274-2
MathSciNet review: 667274
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Abstract: Smalø[2] showed that the index of nilpotency of the endomorphism ring of a module $ {M_R}$ of finite length is bounded by the number $ \max \left\{ {{n_A}\vert{A_R}\;{\text{simple}}} \right\}$, where $ {n_A}$ denotes the number of times $ {A_R}$ occurs as a factor in a composition chain of $ {M_R}$. We give another proof of Smalø's theorem which leads to an analogous result for artinian modules whose homogeneous length is finite.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0667274-2
Keywords: Endomorphism ring, index of nilpotency
Article copyright: © Copyright 1982 American Mathematical Society