Nil subrings of endomorphism rings of modules

Fisher, Joe W.

doi:10.1090/S0002-9939-1972-0292878-2

Nil subrings of endomorphism rings of modules
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by Joe W. Fisher

Proc. Amer. Math. Soc. 34 (1972), 75-78

DOI: https://doi.org/10.1090/S0002-9939-1972-0292878-2

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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

Joe W. Fisher, On the nilpotency of nil subrings, Canadian J. Math. 22 (1970), 1211–1216. MR 268216, DOI 10.4153/CJM-1970-139-1
Joe W. Fisher, Nil subrings with bounded indices of nilpotency, J. Algebra 19 (1971), 509–516. MR 289554, DOI 10.1016/0021-8693(71)90083-4

Endomorphism rings of modules

18

A note on rings of endomorphisms

Joachim Lambek, Lectures on rings and modules, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. With an appendix by Ian G. Connell. MR 0206032
Claudio Procesi and Lance Small, Endomorphism rings of modules over $\textrm {PI}$-algebras, Math. Z. 106 (1968), 178–180. MR 233846, DOI 10.1007/BF01110128