A theorem of complete reducibility for exponential polynomials

TL;DR

This paper extends Ritt's factorization theorem to the ring of exponential polynomials in multiple variables over an algebraically closed field of characteristic zero, providing a new understanding of their structure.

Contribution

The paper generalizes Ritt's factorization theorem to multivariable exponential polynomials over algebraically closed fields of characteristic zero.

Findings

Established a new factorization theorem for exponential polynomials in multiple variables.

Extended classical results to a broader algebraic setting.

Provided a foundation for further algebraic and computational studies of exponential polynomials.

Abstract

In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due to Ritt in \cite{ritt}.