On radical unitary ideals of rings of integer-valued polynomials

Abstract

Let D be a Dedekind domain (not a field) with finite residue fields and let $\mathrm{Int}\left(D\right)$ be the ring of integer-valued polynomials over D. We completely classify in topological terms some relevant classes of radical unitary ideals of $\mathrm{Int}\left(D\right)$ (and of its overrings). This project strongly extends the classification given in a previous paper and regarding special unitary ideals, precisely the ones lying over a given maximal ideal of D.