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Generating ideals in rings of integer-valued polynomials - MaRDI portal

Generating ideals in rings of integer-valued polynomials (Q1073835)

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scientific article; zbMATH DE number 3946266
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English
Generating ideals in rings of integer-valued polynomials
scientific article; zbMATH DE number 3946266

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    Generating ideals in rings of integer-valued polynomials (English)
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    1985
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    Let K be an algebraic number field with integers A. The author considers the subring of the polynomial ring K[X] consisting of the polynomials for which f(A)\(\subseteq A\). For this ring of ''integer-valued polynomials'' the author proves that every finitely generated ideal can be generated by two elements. This extends a result by \textit{R. Gilmer} and the reviewer [J. Algebra 81, 150-164 (1983; Zbl 0515.13016)] for the case K being the rational numbers. An additional extension of this result to a more general class of Dedekind domains can be found in a paper by \textit{D. L. McQuillan} [J. Reine Angew. Math. 358, 162-178 (1985; Zbl 0568.13003)].
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    algebraic number field
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    integer-valued polynomials
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    finitely generated ideal
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