Exponential polynomials and polynomial equations.

Abstract

Additive functions play an important role not only in functional equations but also in the field of (commutative) algebra. It is an important and challenging question how special morphisms can be characterized among additive mappings in general. The study of additive mappings from a ring into another ring which preserves squares was initiated by G. Ancochea. Later, these results were strengthened by many. However, such questions can also be raised in connection with generalized polynomials, too. We consider generalised monomial functions satisfying complex polynomial identities involving multiple variables. Our goal is to explore whether such identities imply a specific form for the involved functions and to develop methods for identifying these forms.