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)

 
 

 

The general solution of a first order differential polynomial


Author: Richard M. Cohn
Journal: Proc. Amer. Math. Soc. 55 (1976), 14-16
DOI: https://doi.org/10.1090/S0002-9939-1976-0396511-4
MathSciNet review: 0396511
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: A purely algebraic proof is given of a theorem, proved analytically by Ritt, which determines the number of derivations needed to find a basis for the perfect ideal of the general solution of an algebraically irreducible first order differential polynomial.


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

  • [1] E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York and London, 1973. MR 0568864 (58:27929)
  • [2] J. F. Ritt, Differential algebra, Amer. Math. Soc. Colloq. Publ., vol. 33, Amer. Math. Soc., Providence, R.I., 1950. MR 12, 7. MR 0035763 (12:7c)
  • [3] A. Seidenberg, Abstract differential algebra and the analytic case, Proc. Amer. Math. Soc. 9(1958), 159-164. MR 20 #178. MR 0093655 (20:178)
  • [4] -, Abstract differential algebra and the analytic case. II, Proc. Amer. Math. Soc. 23(1969), 689-691. MR 40 #1376. MR 0248122 (40:1376)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0396511-4
Keywords: General solution, singular components, basis for a perfect differential ideal
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society