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Interpolation by Integer-Valued Polynomials

โœ Scribed by Sophie Frisch


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
177 KB
Volume
211
Category
Article
ISSN
0021-8693

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Let R be a Dedekind domain whose residue fields are finite, and let K be the field of fractions of R. When S is a (non-empty) subset of K we write Int(S) for the subring of K[X ] consisting of all polynomials f (X ) in K[X] such that f (S ) R. We show that there exist fractional ideals J 0 , J 1 , .

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Let A be a Dedekind domain with finite residue fields, K it's quotient field, L a finite separable extension of K, and B the integral closure of A in L. The rings of integer-valued polynomials on A and B are known to be Pru fer domains and will be denoted by Int(A) and Int(B), respectively. We will

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Let \(R\) be a Dedekind domain with field of fractions \(K, L=K(x)\) a finite separable extension of \(K\), and \(S\) the integral closure of \(R\) in \(L\). Let \(I\) be the subring of \(K[X]\) consisting of all polynomials \(g(x)\) in \(K[X]\) such that \(g(R) \subset R\), and let \(E_{x}: I \righ

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Let D be a domain with quotient field K. We consider the ring Int D [ f g w x ลฝ . x K X ; f D : D of integer-valued polynomial rings over D. We completely ลฝ . characterize the domains D for which Int D is a Prufer ยจ-multiplication domain. แฎŠ

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Let R be a domain and K its quotient-field. For a subset S of K, let F R (S) be the set of polynomials f # K[x] with f (S ) R and define the R-closure of S as the set of those t # K for which f (t) # R for all f # F R (S ). The concept of R-closure was introduced by McQuillan (J. Number Theory 39 (1