Geodesic
A Theorem on Derivations of Prime Rings with Involution
Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 356-369

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

In a recent note [2] we showed that if R is a prime ring and d ≠ 0 a derivation of R such that d(x)d(y) = d(y)d(x) for all x, y ∈ R then, if R is not a characteristic 2, R must be commutative. (If char R = 2 we showed that R must be an order in a 4-dimensional simple algebra.)In this paper we shall consider a similar problem, namely, that of a prime ring R with involution * where d(x)d(y) = d(y)d(x) not for all x, y ∈ R but merely for symmetric elements x* = x and y* = y. Although it is clear that some results can be obtained if R is of characteristic 2, we shall only be concerned with the case char R ≠ 2. Even in this case one cannot hope to extend the result cited in the first paragraph, that is, to show that R is commutative. 
Herstein, I. N. A Theorem on Derivations of Prime Rings with Involution. Canadian journal of mathematics, Tome 34 (1982) no. 2, pp. 356-369. doi: 10.4153/CJM-1982-023-x
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[1] 1. Bergen, J., Herstein, I. N. and Kerr, J. W., Lie ideals and derivations of prime rings, (to appear). Google Scholar

[2] 2. Herstein, I. N., A note on derivations, Canadian Math. Bull. 21 (1978), 369–370. Google Scholar

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