zbMATH — the first resource for mathematics

On generalized higher derivations. (English) Zbl 0979.16022
The author introduces the concept of a generalized higher derivation in such a way that it extends the well-known concept of a higher derivation as well as the concept of a generalized derivation as introduced by the same author [in Sci. Math. 2, No. 3, 345-352 (1999; Zbl 0968.16018)]. Moreover, somewhat more general concepts of generalized higher Jordan (resp. Lie) derivations are also introduced. Various elementary properties of generalized higher (Jordan, Lie) derivations are discussed.

16W25 Derivations, actions of Lie algebras
16W10 Rings with involution; Lie, Jordan and other nonassociative structures