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Nilpotency of derivations in prime rings
1995
Proceedings of the American Mathematical Society
In 1957, E. C. Posner proved that if X and ô are derivations of a prime ring R, characteristic R / 2, then XS = 0 implies either X = 0 or S = 0. We extend this well-known result by showing that, without any characteristic restriction, Xôm = 0 implies either X = 0 or <54m_1 = 0. We also prove that XnS = 0 implies either S2 = 0 or A12"-9 = 0. In the case where X"ôm = 0 , we show that if X and ô commute, then at least one of the derivations must be nilpotent. A derivation of a ring 7? is an
doi:10.1090/s0002-9939-1995-1291775-9
fatcat:hqci2hd7yjbjvf6pen2w2ca3zm