Generalized Functional Identities with (Anti-)Automorphisms and Derivations on Prime Rings, I,

The concept of a generalized functional identity (GFI) with (anti)automorphisms and derivations is a generalization of the notion of a generalized polynomial identity (GPI) with (anti)automorphisms and derivations. In the present paper we show that either a prime ring is GPI or such GFIs have only the “obvious” solutions. Our results simultaneously generalize the results of Martindale, Rowen, Lanski, Kharchenko, and Chuang on GPIs and a number of earlier results on GFIs.