Generating ideals in rings of integer-valued polynomials
Let K be an algebraic number field with integers A. The author considers the subring of the polynomial ring K[X] consisting of the polynomials for which f(A)\(\subseteq A\). For this ring of ''integer-valued polynomials'' the author proves that every finitely generated ideal can be generated by two elements. This extends a result by \textit{R. Gilmer} and the reviewer [J. Algebra 81, 150-164 (1983; Zbl 0515.13016)] for the case K being the rational numbers. An additional extension of this result to a more general class of Dedekind domains can be found in a paper by \textit{D. L. McQuillan} [J. Reine Angew. Math. 358, 162-178 (1985; Zbl 0568.13003)].
scientific article; zbMATH DE number 3946266