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A Condition for the Commutativity ofRings

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein
I. N. Herstein*
Affiliation:
Yale University
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A well-known theorem of Jacobson (1) asserts that if every element a of a ring A satisfies a relation an(a) = a where n(a) > 1 is an integer, then A is a commutative ring. Thus the condition used in Jacobson's theorem is a sufficient condition for commutativity. However the condition is by no means a necessary one, as it is satisfied by a very restricted class of commutative rings.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 583 - 586
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Jacobson, N., Structure theory for algebraic algebras of bounded degree, Ann. Math., 46 (1945), 695–707.Google Scholar