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A note on Jacobson's conjecture for right Noetherian rings

Published online by Cambridge University Press:  18 May 2009

K. A. Brown  and
T. H. Lenagan
K. A. Brown
Affiliation:
University of Glasgow
T. H. Lenagan
Affiliation:
University of Edinburgh
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In 1956, Jacobson asked whether the intersection of the powers of the Jacobson radical, J(R), of a right Noetherian ring R, must always be zero [4, p. 200]. His question was answered in the negative by I. N. Herstein [3], who noted that , where Z(2) denotes the ring of rational numbers with denominator prime to 2, affords a counterexample. In contrast, the ring , though similar in appearance to R1, satisfies . (Here, k denotes a field.)

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 1 , January 1982 , pp. 7 - 8
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

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