Construction, sur un anneau de Dedekind, d'une base régulière de polynômes à valeurs entières. (Construction of a regular base of integer valued polynomials over a Dedekind ring)
Using a result of \textit{P.-J. Cahen} [Can. J. Math. 24, 747-754 (1972; Zbl 0224.13006)] which characterizes Dedekind domains A such that the ring \(A[X]_{sub}\) of integer valued polynomials over A admits a basis \(Q_ 0(X),Q_ 1(X),...,Q_ n(X),..\). such that \(\deg (Q_ n(X))=n\) for any n, the author constructs explicitly such a basis. The construction depends essentially on a result of \textit{G. Pólya} which states that for such Dedekind domains and any integer n the ideal of leading coefficients of integer valued polynomials over A of degree \(\leq n\) is principal.
scientific article; zbMATH DE number 4144106