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Proceedings of the American Mathematical Society
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0784161-2
PII: S 0002-9939(1985)0784161-2
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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