Generalized rational identities with automorphisms, antiautomorphisms, and derivations. (Q1768179)

The author generalizes the notion of generalized identity and considers generalized rational identities incorporating automorphisms, antiautomorphisms, and derivations. The main results give that, under certain restrictions, a division ring satisfying a generalized rational identity of the kind considered, is finite dimensional over its centre. As a consequence, if a division ring is infinite dimensional over its centre, then the nontrivial (in some natural sense) generalized rational identities incorporating mappings, are equivalent to ``ordinary'' generalized rational identities.