Prime and maximal ideals in Hurwitz polynomial rings

TL;DR

This paper characterizes prime and maximal ideals in Hurwitz polynomial rings, providing conditions for their existence and methods to identify maximal ideals generated by minimal degree polynomials.

Contribution

It offers a new characterization for R-disjoint prime ideals and explores conditions for the existence and determination of maximal ideals in Hurwitz polynomial rings.

Findings

Characterization of R-disjoint prime ideals.

Conditions for the existence of maximal ideals.

Method to determine maximal ideals generated by minimal degree polynomials.

Abstract

In this paper we study prime and maximal ideals in a Hurwitz polynomial ring hR. It is well-known that to study many questions we may assume R is prime and consider just R-disjoint ideals. We give a characterization for an R-disjoint ideal to be prime. We study conditions under which there exists an R-disjoint ideal which is a maximal ideal and when this is the case how to determine all such maximal ideals. maximal ideal to be generated by polynomials of minimal degree.