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Un anneau de Prüfer
H. Lombardi1
1 Équipe de Mathématiques, UMR CNRS 6623, UFR des Sciences et Techniques, Université de Franche-Comté, 25030 BESANCON cedex, FRANCE
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 59-69.

Let E be the ring of integer valued polynomials over 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.

Published online:
DOI: 10.5802/acirm.35
Classification: 13F05, 13F20, 13A15, 03F65
Keywords: Prüfer rings, Integer-valued polynomials, Constructive mathematics.
H. Lombardi 1

1 Équipe de Mathématiques, UMR CNRS 6623, UFR des Sciences et Techniques, Université de Franche-Comté, 25030 BESANCON cedex, FRANCE 
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     zbl = {1439.13046},
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H. Lombardi. Un anneau de Prüfer. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 59-69. doi : 10.5802/acirm.35. https://acirm.centre-mersenne.org/articles/10.5802/acirm.35/

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