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Determining integer-valued polynomials from their image. (English) Zbl 1439.13047

Summary: This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with S. T. Chapman, and appeared in [J. Algebra 348, No. 1, 350–353 (2011; Zbl 1239.11029)]. Let \(\operatorname{Int}(\mathbb Z)\) represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on \(\mathbb Z\).

MSC:

13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
11C08 Polynomials in number theory
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13G05 Integral domains
13B25 Polynomials over commutative rings

Citations:

Zbl 1239.11029
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References:

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[2] Scott T. Chapman and Vadim Ponomarenko, \(On image sets of integer-valued polynomials\), submitted. · Zbl 1239.11029
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