Existence of GCD's and Factorization in Rings of Non-Archimedean Entire Functions

TL;DR

This paper proves that rings of non-Archimedean entire functions of several variables have GCDs and are nearly factorial, allowing unique factorization into irreducible functions.

Contribution

It provides a detailed proof of GCD existence and near-factoriality in rings of non-Archimedean entire functions, extending known algebraic properties.

Findings

GCDs exist in these rings

Rings are almost factorial

Unique factorization into irreducibles

Abstract

A detailed proof is given of the well-known facts that greatest common divisors exist in rings of non-Archimedean entire functions of several variables and that these rings of entire functions are almost factorial, in the sense that an entire function can be uniquely written as a countable product of irreducible entire functions.