Mori domains of integer-valued polynomials

Abstract

Let D be a domain with quotient field K. We investigate conditions under which the ring Int(D)={f∈K[X] | f(D)⊆D} of integer-valued polynomials over D is a Mori domain. In particular, we show that if D is a pseudo-valuation domain with finite residue field such that the associated valuation overring is rank one discrete and has infinite residue field, then Int( D) is a Mori domain with Int( D)≠ D[ X]. Finally, we investigate the class group of a Mori domain of integer-valued polynomials, showing, in the case just mentioned, that Cl(Int( D)) is generated by the classes of the t-maximal uppers to zero.