Un anneau de Prüfer

Lombardi, H.

Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 59-69.

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.

Classification : 13F05, 13F20, 13A15, 03F65
Mots clés : Prüfer rings, Integer-valued polynomials, Constructive mathematics.

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