Nil and strongly nil derivations |
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Authors: | LO Chung |
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Institution: | Mathematics Department , North Carolina State University , P. O. Box 8205, Raleigh, North Carolina, 27695-8205 |
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Abstract: | In a semiprime algebra R over a field of characteristic p ≥ 0, a derivation d is called nil if for each x ? R there is n such that dnx = 0. It is called strongly nil if it is induced by a nil element in the symmetric ring of quotients. The first result of this paper is an intrinsic criterion on a nil derivation being strongly nil. We then use this criterion to establish some relation between a nilpotent derivation and a strongly nilpotent derivation after a preliminary discussion of the nilpotency, or index of nilpotency, of a nilpotent derivation. Examples are given later in the paper to show that in some sense these results are best possible. This paper is self contained. |
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