On a generalization of de Rham lemma
Kyoji Saito (1976)
Annales de l'institut Fourier
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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.