Let be a free module over a noetherian ring. For , let be the ideal generated by coefficients of . For an element with , if , there exists such that .
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.
Soit un module libre sur un anneau noethérien. Pour , soit l’idéal engendré par les coefficients de . Si est un élément de avec et si , il existe tels que .
Ceci généralise un lemme de de Rham sur la division des formes (Comment. Math. Helv., 28 (1954)) et on en obtient quelques applications à l’étude des singularités.
@article{AIF_1976__26_2_165_0, author = {Saito, Kyoji}, title = {On a generalization of de {Rham} lemma}, journal = {Annales de l'Institut Fourier}, pages = {165--170}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {26}, number = {2}, year = {1976}, doi = {10.5802/aif.620}, mrnumber = {54 #1276}, zbl = {0338.13009}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.620/} }
TY - JOUR AU - Saito, Kyoji TI - On a generalization of de Rham lemma JO - Annales de l'Institut Fourier PY - 1976 SP - 165 EP - 170 VL - 26 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.620/ DO - 10.5802/aif.620 LA - en ID - AIF_1976__26_2_165_0 ER -
Saito, Kyoji. On a generalization of de Rham lemma. Annales de l'Institut Fourier, Volume 26 (1976) no. 2, pp. 165-170. doi : 10.5802/aif.620. http://archive.numdam.org/articles/10.5802/aif.620/