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On Simple Rings with Maximal Annihilator Right Ideals

Published online by Cambridge University Press:  20 November 2018

Kwangil Koh
Kwangil Koh*
Affiliation:
N. C. State University at Raleigh Raleigh N. C
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If R is a simple ring with 1 which contains a maximal annihilator right ideal then R is the endomorphism ring of a unital torsion-free module over an integral domain.

We first prove the following:

Let R be a ring with 1. If a ϵ R such that (a)r = {r ϵ R|ar = 0} is a maximal annihilator right ideal then HomR(aR, aR) is an integral domain.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 667 - 668
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Jacobson, N., Structure of Rings, Amer. Math. Soc. Colloquium Publication (1956).Google Scholar