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On Derivations in Prime Rings and a Question of Herstein

Published online by Cambridge University Press:  20 November 2018

Amos Kovacs
Amos Kovacs*
Affiliation:
Dept. of Mathematics, Technion I.I.T. Haifa, Israel
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In [2], Herstein proves the following result:

Theorem. Let R be a prime ring, d≠0 a derivation of R such that d(x) d(y) = d(y) d(x) for all x, y ∈ R. Then, if char r≠2, R is commutative, and if char R = 2, R is commutative or an order in a simple algebra which is 4-dimensional over its center.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 339 - 344
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Belluce, L. P. and Jain, S. K., Prime rings with a one sided ideal satisfying a polynomial identity, Pacific J. Math. vol. 24, No. 3, 1968, pp. 421-424.Google Scholar
2. Hernstein, I. N., A note on derivations, to appear.Google Scholar