Localizations of integer‐valued polynomials and of their Picard group

DOI10.1002/mana.202200208arXiv2205.11312OpenAlexW4383721784MaRDI QIDQ6144875

Dario Spirito

Publication date: 8 January 2024

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.11312

zbMATH Keywords

Picard groupinteger-valued polynomialsPrüfer domainsalmost Dedekind domainsJaffard family

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Class groups (13C20)

Cites Work

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• Factoring ideals in integral domains
• Abstract Riemann surfaces of integral domains and spectral spaces
• The conditions \(\text{Int}(R)\subseteq R_S[X\) and \(\text{Int}(R_S)=\text{Int}(R)_S\) for integer-valued polynomials]
• Mori domains of integer-valued polynomials
• Jaffard families and localizations of star operations
• The derived sequence of a pre-Jaffard family
• Decomposition and classification of length functions
• Almost Dedekind domains without radical factorization
• Integer-Valued Polynomials
• Topology, intersections and flat modules
• Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings
• Integer-Valued Polynomial Rings,t-Closure, and Associated Primes
• Integer-Valued Polynomials, Prufer Domains, and Localization
• The Ring of Integer-Valued Polynomials of a Dedekind Domain
• Spectral Spaces
• Abelian Groups
• Spectral Spaces and Ultrafilters
• Remarks on generalized rings of quotients
• Generalized Quotient Rings

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