Interpolation Domains

✍ Scribed by Paul-Jean Cahen; Jean-Luc Chabert; Sophie Frisch

• Book ID: 102576282
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 88 KB
• Volume: 225
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.8151

✦ Synopsis

Call a domain D with quotient field K an interpolation domain if, for each choice of distinct arguments a , . . . , a and arbitrary values c , . . . , c in D, there

We characterize completely the interpolation doi i mains if D is Noetherian or a Prufer domain. In the first case, we show that D is än interpolation domain if and only if it is one-dimensional, locally unibranched Ž . Ä with finite residue fields, in the second one, if and only if the ring Int D s f g w x< Ž . 4 K X f D : D of integer-valued polynomials is itself a Prufer domain. We also show that an interpolation domain must satisfy a double-boundedness condition, Ž . and thereby simplify a recent characterization of the domains D such that Int D is a Prufer domain.