Prüfer intersection of valuation domains of a field of rational functions

DOI10.1016/j.jalgebra.2018.05.012zbMath1394.13022arXiv1711.05485OpenAlexW2770584732MaRDI QIDQ1643188

Giulio Peruginelli

Publication date: 18 June 2018

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.05485

zbMATH Keywords

Prüfer domaininteger-valued polynomialresidually transcendental extensionpseudo-limitpseudo-monotone sequence

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Valuations and their generalizations for commutative rings (13A18) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (7)

Globalized pseudo-valuation domains of integer-valued polynomials on a subset ⋮ Polynomial Dedekind domains with finite residue fields of prime characteristic ⋮ The Zariski–Riemann space of valuation domains associated to pseudo-convergent sequences ⋮ Prüfer domains of integer-valued polynomials and the two-generator property ⋮ Extending valuations to the field of rational functions using pseudo-monotone sequences ⋮ Integer-valued polynomials, Prüfer domains and the stacked bases property ⋮ Metrizability of spaces of valuation domains associated to pseudo-convergent sequences

Cites Work

• Pseudo-convergent sequences and Prüfer domains of integer-valued polynomials
• A theorem of characterization of residual transcendental extensions of a valuation
• All valuations on K(X)
• On the polynomial closure in a valued field
• A principal ideal theorem for compact sets of rank one valuation rings
• Untersuchungen zur arithmetischen Theorie der Körper. (Die Theorie der Teilbarkeit in allgemeinen Körpern. I-III.)
• Prüfer domains of integer-valued polynomials on a subset
• On the geometry of Prüfer intersections of valuation rings
• Maximal fields with valuations
• Integer-Valued Polynomials
• Prüfer Domains of Integer-Valued Polynomials
• Principal ideal theorems for holomorphy rings in fields.
• A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain
• Value groups, residue fields, and bad places of rational function fields
• Transcendental extensions of a valuation domain of rank one
• Two constructions of prüfer domains.
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