Height one differential ideals in polynomial rings
HTML articles powered by AMS MathViewer
- by Matthew S. Chen PDF
- Proc. Amer. Math. Soc. 86 (1982), 561-566 Request permission
Abstract:
Let $D$ be a derivation of a polynomial ring $k[{X_1}, \ldots ,{X_n}]$ with $k$ a field of characteristic 0 and $Dk = \{ 0\}$. If infinitely many principal prime ideals $(f)$ satisfy $Df \in (f)$, then every maximal ideal contains such an $(f)$.References
- J. P. Jouanolou, Équations de Pfaff algébriques, Lecture Notes in Mathematics, vol. 708, Springer, Berlin, 1979 (French). MR 537038
- Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. MR 0100591 H. Poincaré, Sur l’intégration algébrique des équations différentielles du premier ordre et du premier degré, Rend. Circ. Mat. Palermo 5 (1891), 161-191; 11 (1897), 193-239; reprinted in Oeuvres de Henri Poincaré, tome III, Gauthier-Villars, Paris, 1934, pp. 35-58, 59-94.
- A. Seidenberg, Differential ideals in rings of finitely generated type, Amer. J. Math. 89 (1967), 22–42. MR 212027, DOI 10.2307/2373093
- Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0120249
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 561-566
- MSC: Primary 13N05; Secondary 13F20
- DOI: https://doi.org/10.1090/S0002-9939-1982-0674081-3
- MathSciNet review: 674081