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 \(\mathbb Z\).


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


Zbl 1239.11029
Full Text: DOI


[1] Paul-Jean Cahen, Jean-Luc Chabert, and Sophie Frisch, \(Interpolation domains\), J. Algebra 225 (2000), no. 2, 794-803. MR 1741562 (2001b:13024) · Zbl 0990.13014
[2] Scott T. Chapman and Vadim Ponomarenko, \(On image sets of integer-valued polynomials\), submitted. · Zbl 1239.11029
[3] Sophie Frisch, \(Interpolation by integer-valued polynomials\), J. Algebra 211 (1999), no. 2, 562-577. MR 1666659 (99m:13016) · Zbl 0927.13023
[4] G. Peruginelli and U. Zannier, \(Parametrizing over \)\Bbb Z\( integral values of polynomials over \)\Bbb Q\[, Comm. Algebra 38 (2010), no. 1, 119-130. MR 2597485 (2011e:11064) | Copyright Cellule MathDoc 20\] · Zbl 1219.11048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.