On the polynomial closure in a valued field
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Publication:1048940
DOI10.1016/j.jnt.2009.09.016zbMath1245.13014OpenAlexW1981310642MaRDI QIDQ1048940
Publication date: 8 January 2010
Published in: Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jnt.2009.09.016
Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in number theory (11C08) Valuation rings (13F30)
Related Items (11)
Prüfer intersection of valuation domains of a field of rational functions ⋮ The polynomial closure is not topological ⋮ Approximation types describing extensions of valuations to rational function fields ⋮ Regular subsets of valued fields and Bhargava's \(v\)-orderings ⋮ The Zariski–Riemann space of valuation domains associated to pseudo-convergent sequences ⋮ An overview of some recent developments on integer-valued polynomials: Answers and Questions ⋮ Extending valuations to the field of rational functions using pseudo-monotone sequences ⋮ Integer-valued polynomials, Prüfer domains and the stacked bases property ⋮ Topological properties of subsets of the Zariski space ⋮ A survey on fixed divisors ⋮ Metrizability of spaces of valuation domains associated to pseudo-convergent sequences
Cites Work
- Sets that determine integer-valued polynomials
- On a theorem of R. Gilmer
- Polynomial closure
- Polynomial closure in essential domains
- Untersuchungen zur arithmetischen Theorie der Körper. (Die Theorie der Teilbarkeit in allgemeinen Körpern. I-III.)
- Substitution and closure of sets under integer-valued polynomials
- Maximal fields with valuations
- Integer-Valued Polynomials
- The Skolem property in rings of integer-valued polynomials
- Polynomial Closure in Noetherian Pseudo-valuation Domains
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