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Proceedings of the American Mathematical Society

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Nil subrings of endomorphism rings of modules

Author: Joe W. Fisher
Journal: Proc. Amer. Math. Soc. 34 (1972), 75-78
MSC: Primary 16A64
MathSciNet review: 0292878
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Abstract: Let M be an R-module and let $ {\text{End}_R}(M)$ be the ring of all R-endomorphisms of M. If M is Artinian, then each nil subring of $ {\text{End}_R}(M)$ is nilpotent. If M is Noetherian, then the indices of nilpotency of the nil subrings of $ {\text{End}_R}(M)$ are bounded.

References [Enhancements On Off] (What's this?)

  • [1] Joe W. Fisher, On the nilpotency of nil subrings, Canad. J. Math. 22 (1970), 1211–1216. MR 0268216
  • [2] Joe W. Fisher, Nil subrings with bounded indices of nilpotency, J. Algebra 19 (1971), 509–516. MR 0289554
  • [3] -, Endomorphism rings of modules, Notices Amer. Math. Soc. 18 (1971), 619-620. Abstract #71T-A85.
  • [4] A. W. Goldie and L. W. Small, A note on rings of endomorphisms (to appear).
  • [5] Joachim Lambek, Lectures on rings and modules, With an appendix by Ian G. Connell, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0206032
  • [6] Claudio Procesi and Lance Small, Endomorphism rings of modules over 𝑃𝐼-algebras, Math. Z. 106 (1968), 178–180. MR 0233846

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Keywords: Nil ring, T-nilpotent ring, nilpotent ring, endomorphism ring, Artinian module, Noetherian module, injective Noetherian module
Article copyright: © Copyright 1972 American Mathematical Society