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On image sets of integer-valued polynomials

✍ Scribed by Scott T. Chapman; Vadim Ponomarenko


Book ID
113675311
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
122 KB
Volume
348
Category
Article
ISSN
0021-8693

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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

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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 , .