On a generalization of de Rham lemma

Kyoji Saito

Annales de l'institut Fourier (1976)

  • Volume: 26, Issue: 2, page 165-170
  • ISSN: 0373-0956

Abstract

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Let M be a free module over a noetherian ring. For ω 1 , ... , ω k M , let 𝒜 be the ideal generated by coefficients of ω 1 ... ω k . For an element ω p M with p < prof . 𝒜 , if ω ω 1 ... ω k = 0 , there exists η 1 , ... , η k p - 1 M such that ω = i = 1 k η i ω i .This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.

How to cite

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Saito, Kyoji. "On a generalization of de Rham lemma." Annales de l'institut Fourier 26.2 (1976): 165-170. <http://eudml.org/doc/74277>.

@article{Saito1976,
abstract = {Let $M$ be a free module over a noetherian ring. For $\omega _1,\ldots ,\omega _k\in M$, let $\{\cal A\}$ be the ideal generated by coefficients of $\omega _1\wedge \ldots \wedge \omega _k$. For an element $\omega \in \bigwedge ^pM$ with $p&lt; \,\{\rm prof.\}\,\{\cal A\}$, if $\omega \wedge \omega _1\wedge \ldots \wedge \omega _k=0$, there exists $\eta _1,\ldots ,\eta _k\in \bigwedge ^\{p-1\}M$ such that $\omega =\sum ^k_\{i=1\}\eta _i\wedge \omega _i$.This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.},
author = {Saito, Kyoji},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {165-170},
publisher = {Association des Annales de l'Institut Fourier},
title = {On a generalization of de Rham lemma},
url = {http://eudml.org/doc/74277},
volume = {26},
year = {1976},
}

TY - JOUR
AU - Saito, Kyoji
TI - On a generalization of de Rham lemma
JO - Annales de l'institut Fourier
PY - 1976
PB - Association des Annales de l'Institut Fourier
VL - 26
IS - 2
SP - 165
EP - 170
AB - Let $M$ be a free module over a noetherian ring. For $\omega _1,\ldots ,\omega _k\in M$, let ${\cal A}$ be the ideal generated by coefficients of $\omega _1\wedge \ldots \wedge \omega _k$. For an element $\omega \in \bigwedge ^pM$ with $p&lt; \,{\rm prof.}\,{\cal A}$, if $\omega \wedge \omega _1\wedge \ldots \wedge \omega _k=0$, there exists $\eta _1,\ldots ,\eta _k\in \bigwedge ^{p-1}M$ such that $\omega =\sum ^k_{i=1}\eta _i\wedge \omega _i$.This is a generalization of a lemma on the division of forms due to de Rham (Comment. Math. Helv., 28 (1954)) and has some applications to the study of singularities.
LA - eng
UR - http://eudml.org/doc/74277
ER -

Citations in EuDML Documents

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  1. Dominique Cerveau, Alcides Lins Neto, Holomorphic foliations in ( 2 ) having an invariant algebraic curve
  2. Jean-Pierre Ramis, Frobenius avec singularités
  3. Jean-François Mattei, Robert Moussu, Intégrales premières d'une forme de Pfaff analytique
  4. F. Cukierman, J. V. Pereira, I. Vainsencher, Stability of foliations induced by rational maps
  5. Dominique Cerveau, Paulo R. Sad, Fonctions et feuilletages Levi-Flat. Étude locale
  6. Philippe Bonnet, Relative exactness modulo a polynomial map and algebraic ( p , + ) -actions
  7. Andrzej Weber, Leray residue for singular varieties
  8. Dominique Cerveau, Distributions involutives singulières
  9. Dominique Cerveau, Alcides Lins Neto, Formes tangentes à des actions commutatives
  10. J.-F. Mattei, R. Moussu, Holonomie et intégrales premières

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