Example of an interpolation domain
A domain \(D\) is an interpolation domain if, for every choice of finitely many distinct elements \(a_1,\ldots,a_n\) of \(D\), and arbitrary \(b_1,\ldots,b_n\) in \(D\) there exists a polynomial \(f\in \text{Int}(D)\) with \(f(a_i)=b_i\) for \(1\leq i\leq n\). Here \(\text{Int}(D)\) denotes the ring of integer-valued polynomials on \(D\), i.e.~the ring of polynomials with coefficients in the quotient field of \(D\) with the property \(f(d)\in D\) for every \(d\in D\). The author gives an example of an interpolation domain whose integral closure is not an interpolation domain, thereby answering a question posed by \textit{P.-J. Cahen, J.-L. Chabert} and \textit{S. Frisch} [J. Algebra 225, No. 2, 794--803 (2000; Zbl 0990.13014)].
scientific article; zbMATH DE number 1839053