Generalized exponential polynomials and functional equations

Debreceni Egyetem

Matematika- és Számítástudományok Doktori Iskola

Gselmann Eszter

matematika- és számítástudományok

Functional equations satisfied by additive functions play an important role not only in the theory of functional equations, but also in the theory of (commutative) algebra. It is an important and challenging question how special morphisms (such as homomorphisms and derivations) can be characterized among additive mappings in general. The study of additive mappings from a ring into another ring which preserve squares was initiated by G. Ancochea in connection with problems arising in projective geometry. Later, these results were strengthened by (among others) I. Kaplansky and N. Jacobson jointly with C. Rickart. However, such and similar questions can be raised not only in connection with additive functions, but also in connection with generalized polynomials, too. More concretely, assume that n is a fixed positive integer and f is a generalized polynomial of degree n mapping between (commutative) fields such that f(P(x))=Q(f(x)) holds for some fixed polynomials P and Q. The question in general is whether this mapping can (or cannot) be decomposed with the aid of homomorphisms and/or derivations.

1 fő

UD IM

2022-11-15

Generalized exponential polynomials and functional equations