GENERALIZED HIGHER -DERIVATIONS
Let R be a ring not necessarily with an identity element. A well-known result proved by I. N. Herstein concerning derivations in prime rings have been extensively studied by many authors. Also, M. Ferrero and C. Haetinger extended this result to higher derivations. The main purpose of this work is to introduce the concept of -derivations and generalized -derivations. Then we extend Awtar�s theorem to higher -derivations and to generalized higher -derivations by giving corresponding definitions.
higher derivations, higher -derivations, generalized higher derivations, Lie ideals, prime rings.