Abstract
The ring 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 are characterized by their ideals of values and is a two-dimensional Prüfer domain.
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