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A Prüfer ring. (Un anneau de Prüfer.) (French. English summary) Zbl 1439.13046

Summary: Let \(E\) be the ring of integer valued polynomials over \(\mathbb Z\). This ring is known to be a Prüfer domain. But it seems there does not exist an algorithm for inverting a nonzero finitely generated ideal of \(E\). In this note we show how to obtain such an algorithm by deciphering a classical abstract proof that uses localisations of \(E\) at all prime ideals of \(E\). This confirms a general program of deciphering abstract classical proofs in order to obtain algorithmic proofs.

MSC:

13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13A15 Ideals and multiplicative ideal theory in commutative rings
03F65 Other constructive mathematics
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References:

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