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A Proof of Jacobson’s Theorem

Published online by Cambridge University Press:  20 November 2018

S. W. Dolan
S. W. Dolan*
Affiliation:
Oxford University, Oxford, England
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Abstract

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Let R be a ring such that, for each element a of R, there exists a positive integer n(a) > 1, depending on a, such that an(a)=a. Jacobson proved that such a ring R is necessarily commutative and the purpose of this paper is to give a proof of Jacobson’s Theorem that does not involve the use of the axiom of choice.

We take this opportunity to point out that all rings are assumed to be associative and that nothing beyond elementary ring theory is assumed in the proof to follow. Such ring theory can be found, for example, in [1].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 59 - 61
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Herstein, I. N., Topics in Algebra, Ginn Blaisdell, 1964.Google Scholar