@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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    dct:description """
              Let $K$ be a number field of degree $n$ with ring of integers $O_K$. We show that, if $h\\in K[X]$ maps every element of $O_K$ of degree $n$ to an algebraic integer, then $h(X)$ is integral-valued over $O_K$, that is $h(O_K)\\subset O_K$. We also prove that a similar property holds for a polynomial $f\\in\\mathbb{Q}[X]$ when we consider the set of all algebraic integers $\\alpha$ of degree $n$: if $f(\\alpha)$ is integral over $\\Z$ for every such an $\\alpha$, then $f(\\beta)$ is integral over $\\Z$ for every algebraic integer $\\beta$ of degree smaller than $n$. The result is established by proving that the ring of integer-valued polynomials over the set of matrices $M_n(\\mathbb{Z})$ has integral closure equal to the ring of polynomials in $\\mathbb{Q}[X]$ which are integral-valued over the set of algebraic integers of degree equal to $n$.
            """ ;
    dct:identifier "hal-00796333" ;
    dct:issued "2026-05-13T18:33:10.455980"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-13T18:33:10.455989"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Integral-valued polynomials over the set of algebraic integers of bounded degree" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
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    dcat:keyword "algebraic-integers-with-bounded-degree",
        "infoeu-reposemanticspreprint",
        "integer-valued-polynomial",
        "integral-closure",
        "mathmath-ntmathematics-mathnumber-theory-mathnt",
        "msc-13b25-13f20-11c",
        "polynomial-closure",
        "polynomially-dense-subset",
        "preprints-working-papers-",
        "prufer-domain" ;
    dcat:landingPage <https://hal.science/hal-00796333> .

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    dct:format "HTML" ;
    dct:issued "2026-05-13T18:33:10.461730"^^xsd:dateTime ;
    dct:modified "2026-05-13T18:33:10.404940"^^xsd:dateTime ;
    dct:title "Integral-valued polynomials over the set of algebraic integers of bounded degree" ;
    dcat:accessURL <https://hal.science/hal-00796333> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
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