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Article dans une revue

An Elementary Proof of the Two-Generator Property for the Ring of Integer-Valued Polynomials

Abstract : The ring Int(Z) of integer-valued polynomials has the two-generator property, which means that every finitely generated ideal may be generated by two elements. As the known proofs of this fact are rather complicated using strong topological arguments, we propose here a constructive proof obtained by means of elementary tools. Along the way, we also obtain constructive proofs of two other well-known facts: the finitely generated ideals of Int(Z) are characterized by their ideals of values and Int(Z) is a two-dimensional Prufer domain.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03621210
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Soumis le : lundi 28 mars 2022 - 09:37:46
Dernière modification le : mercredi 14 septembre 2022 - 17:02:26

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Jacques Boulanger, Jean-Luc Chabert. An Elementary Proof of the Two-Generator Property for the Ring of Integer-Valued Polynomials. The American Mathematical Monthly, Mathematical Association of America, 2021, 128 (4), pp.360-366. ⟨10.1080/00029890.2021.1867464⟩. ⟨hal-03621210⟩

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