Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Nilpotency in endomorphism rings

Author: Robert Gordon
Journal: Proc. Amer. Math. Soc. 45 (1974), 38-40
MSC: Primary 16A22
MathSciNet review: 0346000
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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

  • [1] J. W. Fisher, Nil subrings of endomorphism rings of modules, Proc. Amer. Math. Soc. 34 (1972), 75-78. MR 45 #1960. MR 0292878 (45:1960)
  • [2] E. H. Feller and M. G. Deshpande, Endomorphism ring of essential extension of a noetherian module, 1973 (preprint). MR 0346013 (49:10739)
  • [3] A. W. Goldie and L. W. Small, A note on rings of endomorphisms, J. Algebra 24 (1973), 392-395. MR 0308180 (46:7295)
  • [4] R. Gordon and J. C. Robson, Krull dimension, Mem. Amer. Math. Soc. No. 133 (1973). MR 0352177 (50:4664)
  • [5] -, The Gabriel dimension of a module, J. Algebra (to appear). MR 0369425 (51:5658)
  • [6] T. H. Lenagan, The nil radical of a ring with Krull dimension (to appear). MR 0327825 (48:6167)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A22

Retrieve articles in all journals with MSC: 16A22

Additional Information

Keywords: Module with Krull dimension, Krull dimension sequence, endomorphism ring, nil ring, nilpotent ring, artinian object, Grothendieck category, noetherian module, noetherian ring, ring of quotients
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society