Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Height one differential ideals in polynomial rings

Author: Matthew S. Chen
Journal: Proc. Amer. Math. Soc. 86 (1982), 561-566
MSC: Primary 13N05; Secondary 13F20
MathSciNet review: 674081
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [J] J. P. Jouanolou, Équations de Pfaff algébriques, Lecture Notes in Mathematics, vol. 708, Springer, Berlin, 1979 (French). MR 537038
  • [L] Serge Lang, Introduction to algebraic geometry, Interscience Publishers, Inc., New York-London, 1958. MR 0100591
  • [P] 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.
  • [S] A. Seidenberg, Differential ideals in rings of finitely generated type, Amer. J. Math. 89 (1967), 22–42. MR 0212027,
  • [ZS] 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13N05, 13F20

Retrieve articles in all journals with MSC: 13N05, 13F20

Additional Information

Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society