Geodesic
A note on Jacobson's conjecture for right Noetherian rings
Glasgow mathematical journal, Tome 23 (1982) no. 1, pp. 7-8

Voir la notice de l'article provenant de la source Cambridge University Press

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.) 
Brown, K. A.; Lenagan, T. H. A note on Jacobson's conjecture for right Noetherian rings. Glasgow mathematical journal, Tome 23 (1982) no. 1, pp. 7-8. doi: 10.1017/S0017089500004729
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