Nilpotency in endomorphism rings
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- by Robert Gordon PDF
- Proc. Amer. Math. Soc. 45 (1974), 38-40 Request permission
Abstract:
Nil subrings of the endomorphism ring of a module with finite Krull dimension sequence are nilpotent. This includes the case of a module with finite Krull dimension as well as noetherian modules. The method used is to embed the endomorphism ring, modulo a nilpotent ideal, in the endomorphism ring of an artinian object of a Grothendieck category.References
- Joe W. Fisher, Nil subrings of endomorphism rings of modules, Proc. Amer. Math. Soc. 34 (1972), 75–78. MR 292878, DOI 10.1090/S0002-9939-1972-0292878-2
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- Alfred Goldie and Lance W. Small, A note on rings of endomorphisms, J. Algebra 24 (1973), 392–395. MR 308180, DOI 10.1016/0021-8693(73)90147-6
- Robert Gordon and J. C. Robson, Krull dimension, Memoirs of the American Mathematical Society, No. 133, American Mathematical Society, Providence, R.I., 1973. MR 0352177
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 38-40
- MSC: Primary 16A22
- DOI: https://doi.org/10.1090/S0002-9939-1974-0346000-6
- MathSciNet review: 0346000