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

zbMATH Open1233.32012arXiv1007.0984MaRDI QIDQ3100064

William Cherry

Publication date: 22 November 2011

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.

Full work available at URL: https://arxiv.org/abs/1007.0984

zbMATH Keywords

Weierstrass preparation theoremgreatest common divisorsnon-Archimedean entire functions

Mathematics Subject Classification ID

Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15) Entire functions of several complex variables (32A15) Non-Archimedean analysis (32P05)

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