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A Note on Derivations II

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein
I. N. Herstein*
Affiliation:
Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, Illinois60637
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In a previous note on derivations [1] we determined the structure of a prime ring R which has a derivation d≠0 such that the values of d commute, that is, for which d(x) d(y) = d(y) d(x) for all x, y∈R. Perhaps even more natural might be the question: what elements in a prime ring commute with all the values of a non-zero derivation? We address ourselves to this question here, and settle it.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 4 , 01 December 1979 , pp. 509 - 511
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Herstein, I. N., A note on derivations, Canad. Math. Bull. 21 (1978), 369-370.Google Scholar
2. Herstein, I. N., Rings with Involution, University of Chicago Press, Chicago, 1976.Google Scholar