On a generalization of de Rham lemma

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 -