Mori domains of integer-valued polynomials
The authors deal with the problem under which conditions the ring \[ \text{Int} (D)=\{f\in K[X]; f(D)\subseteq D\} \] of integer-valued polynomials over a domain \(D\) with quotient field \(K\) is a Mori domain. If \(D\) is e.g. a Krull domain or a one-dimensional Noetherian domain this question is answered completely because in this case holds: \(\text{Int} (D)=D[X]\) (corollary 2.7 and theorem 3.1). The construction of a domain \(D\) with \(\text{Int} (D)\neq D[X]\) and \(\text{Int} (D)\) a Mori domain is given in \S 3. Further investigations concern the class group of \(\text{Int}(D)\).
scientific article; zbMATH DE number 1526259
scientific article