Ring structure of integer-valued rational functions
Let \(D\) be an integral domain, \(K\) its field of quotients and \(\mathrm{Int}^R(D) = \{f\in K(x):\ f(D)\subset D\}\) its ring of integer-valued rational functions. It has been shown by \textit{A. Loper} and \textit{P. J. Cahen} [J. Pure Appl. Algebra 131, 179--193 (1998; Zbl 0929.13013)] that if \(D\) is a monic or singular Prüfer ring, then \(\mathrm{Int}^R(D)\) is a Prüfer ring. The author presents sufficient conditions for the remaining Prüfer rings to have \(\mathrm{Int}^R(D)\) Prüfer, resp. non-Prüfer. He gives also necessary and sufficient conditions for valuation domains whose ring of integer-valued rational functions is a Prüfer ring, resp. a Bézout ring.
scientific article; zbMATH DE number 7905766