Un anneau de Prüfer

H. Lombardi[1]

  • [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 (2010)

  • Volume: 2, Issue: 2, page 59-69
  • ISSN: 2105-0597

Abstract

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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.

How to cite

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Lombardi, H.. "Un anneau de Prüfer." Actes des rencontres du CIRM 2.2 (2010): 59-69. <http://eudml.org/doc/196278>.

@article{Lombardi2010,
abstract = {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.},
affiliation = {Équipe de Mathématiques, UMR CNRS 6623, UFR des Sciences et Techniques, Université de Franche-Comté, 25030 BESANCON cedex, FRANCE},
author = {Lombardi, H.},
journal = {Actes des rencontres du CIRM},
keywords = {Prüfer rings; Integer-valued polynomials; Constructive mathematics},
language = {fre},
number = {2},
pages = {59-69},
publisher = {CIRM},
title = {Un anneau de Prüfer},
url = {http://eudml.org/doc/196278},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Lombardi, H.
TI - Un anneau de Prüfer
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 59
EP - 69
AB - 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.
LA - fre
KW - Prüfer rings; Integer-valued polynomials; Constructive mathematics
UR - http://eudml.org/doc/196278
ER -

References

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