On the class group of integer-valued polynomial rings over Krull domains
This paper focusses on the property when the class group of a domain is generated by the classes of \(t\)-invertible \(t\)-prime ideals, which holds for Krull domains. On the one hand the authors derive a necessary and sufficient condition for arbitrary domains to possess this property. On the other hand they investigate in this respect the integer-valued polynomial ring over a Krull domain \(D\), \(\text{Int}(D)=\{f\in K[X];f(D)\subseteq D\}\) \((K\) being the quotient field of \(D)\). For example, \(\text{Int}(D)\) has that property if \(D\) has at most finitely many height-one primes with finite residue fields (corollary 2.1).
scientific article; zbMATH DE number 1462309