Ring of endomorphisms of a finite length module
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- by R. N. Gupta and Surjeet Singh
- Proc. Amer. Math. Soc. 94 (1985), 198-200
- DOI: https://doi.org/10.1090/S0002-9939-1985-0784161-2
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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
- 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
Bibliographic 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