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A Note on Power Values of Derivation in Prime and Semiprime Rings

open access: yesJournal of Mathematical Extension, 2012
Let R be a ring with derivation d, such that (d(xy))n = (d(x))n (d(y))n for all x, y ∈ R and n > 1 a fixed integer. In this paper, we show that if R is prime, then d = 0 or R is commutative. If R is semiprime, then d maps R into its center. Moreover
Sh. Sahebi, V. Rahmani
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