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Proceedings of the American Mathematical Society

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



Ring of endomorphisms of a finite length module

Authors: R. N. Gupta and Surjeet Singh
Journal: Proc. Amer. Math. Soc. 94 (1985), 198-200
MSC: Primary 16A65; Secondary 16A05
MathSciNet review: 784161
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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 [Enhancements On Off] (What's this?)

  • [1] C. Faith, Algebra II, Ring theory, Springer-Verlag, Berlin and New York, 1976. MR 0427349 (55:383)
  • [2] M. Harada and T. Ishii, On endomorphism rings of noetherian quasi-injective modules, Osaka J. Math. 9 (1972), 217-223. MR 0318127 (47:6676)

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Keywords: Uniserial modules, ring of endomorphisms, quasi-injective, module, artinian ring, field of fractions
Article copyright: © Copyright 1985 American Mathematical Society

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