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Nilpotency in endomorphism rings

Published:1974 Issue:1 Volume:45 Page:38-40
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Gordon Robert

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-01/S0002-9939-1974-0346000-6/S0002-9939-1974-0346000-6.pdf

Reference6 articles.

1. Nil subrings of endomorphism rings of modules;Fisher, Joe W.;Proc. Amer. Math. Soc.,1972

2. Endomorphism rings of essential extensions of a Noetherian module;Deshpande, M. G.;Israel J. Math.,1974

3. A note on rings of endomorphisms;Goldie, Alfred;J. Algebra,1973

4. Memoirs of the American Mathematical Society, No. 133;Gordon, Robert,1973

5. The Gabriel dimension of a module;Gordon, Robert;J. Algebra,1974

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Endomorphism rings of modules and lattices of submodules;Journal of Soviet Mathematics;1985-11

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