PRIME HIGHER DERIVATIONS ON ALGEBRAS Let A be an algebra. A sequence {d_n} of linear mappings from A into P A is called a higher derivation if d_n(ab) = sum_k=0^n d_k(a) d_{n−k}(b) for each a, b in A and each nonnegative integer n. We say that a sequence {d_n} of linear mappings on A is a prime higher derivation if d_n(ab) = sum_{k|n} d_k(a)d_{n/k} (b) for each a, b in A and each n in N. Giving some examples of prime higher derivations, we establish a characterization of prime higher derivations in terms of derivations.

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