Prime and maximal ideals in Hurwitz polynomial rings

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.