Characterization of Higher Derivations on Algebras

Madjid Mirzavaziri
2010 Communications in Algebra  
Let A be an algebra. A sequence {dn} of linear mappings from A into A is called a higher derivation if dn(ab) = n k=0 d k (a) d n−k (b) for each a, b ∈ A and each nonnegative integer n. We say that a sequence {dn} of linear mappings on A is a prime higher derivation if dn(ab) = k|n d k (a)d n k (b) for each a, b ∈ A and each n ∈ N. Giving some examples of prime higher derivations, we establish a characterization of prime higher derivations in terms of derivations.
doi:10.1080/00927870902828751 fatcat:7xpoasn44zduvdsxwm255fvdua