Nilpotency in endomorphism rings

Gordon, Robert

doi:10.1090/S0002-9939-1974-0346000-6

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
M. G. Deshpande and E. H. Feller, Endomorphism rings of essential extensions of a Noetherian module, Israel J. Math. 17 (1974), 46–49. MR 346013, DOI 10.1007/BF02756823
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
Robert Gordon and J. C. Robson, The Gabriel dimension of a module, J. Algebra 29 (1974), 459–473. MR 369425, DOI 10.1016/0021-8693(74)90081-7
Thomas H. Lenagan, The nil radical of a ring with Krull dimension, Bull. London Math. Soc. 5 (1973), 307–311. MR 327825, DOI 10.1112/blms/5.3.307