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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Ring of endomorphisms of a finite length module
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by R. N. Gupta and Surjeet Singh PDF
Proc. Amer. Math. Soc. 94 (1985), 198-200 Request permission

Abstract:

An example of a uniserial module ${M_R}$ of composition length 2, such that $S = \operatorname {End}({M_R})$ acting on the left is not right artinian, is given. An elementary proof of a known result, that the ring of endomorphism of a finite length quasi-injective module ${M_R}$ acting on the left is left artinian, is also given.
References
  • Carl Faith, Algebra. II, Grundlehren der Mathematischen Wissenschaften, No. 191, Springer-Verlag, Berlin-New York, 1976. Ring theory. MR 0427349
  • Manabu Harada and Tadamasa Ishii, On endomorphism rings of noetherian quasi-injective modules, Osaka Math. J. 9 (1972), 217–223. MR 318127
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 198-200
  • MSC: Primary 16A65; Secondary 16A05
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0784161-2
  • MathSciNet review: 784161