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 congruence lemma for $ [y\sp{p}z]$


Author: Mervin E. Newton
Journal: Proc. Amer. Math. Soc. 38 (1973), 242-246
MSC: Primary 12H05
DOI: https://doi.org/10.1090/S0002-9939-1973-0321913-9
MathSciNet review: 0321913
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A sufficient condition for membership in $ [{y^p}z]$, based on the weight and signature of a term, is given.


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

  • [1] A. P. Hillman, D. G. Mead, K. B. O'Keefe and E. S. O'Keefe, Ideals generated by products, Proc. Amer. Math. Soc. 17 (1966), 717-719. MR 33 #5622. MR 0197457 (33:5622)
  • [2] H. Levi, On the structure of differential polynomials and on their theory of ideals, Trans. Amer. Math. Soc. 51 (1942), 532-568. MR 3, 264. MR 0006163 (3:264f)
  • [3] D. G. Mead, Differential ideals, Proc. Amer. Math. Soc. 6 (1955), 420-432. MR 17, 123. MR 0071417 (17:123d)
  • [4] -, A note on the ideal $ [{y^2}]$, Proc. Amer. Math. Soc. 14 (1963), 607-608. MR 27 #3635. MR 0153674 (27:3635)
  • [5] -, A necessary and sufficient condition for membership in $ [uv]$, Proc. Amer. Math. Soc. 17 (1966), 470-473. MR 33 #5623. MR 0197458 (33:5623)
  • [6] Thomas Muir (revised by W. H. Metzler), A treatise on the theory of determinants, Dover, New York, 1960. MR 22 #5644. MR 0114826 (22:5644)
  • [7] M. E. Newton, The differential ideals $ [{y^p}z]$, Proc. Amer. Math. Soc. 30 (1971), 229-234. MR 44 #2733. MR 0285515 (44:2733)
  • [8] E. S. O'Keefe and K. B. O'Keefe, The differential deal $ [uv]$, Proc. Amer. Math. Soc. 17 (1966), 750-756. MR 33 #5624. MR 0197459 (33:5624)
  • [9] K. B. O'Keefe, A property of the differential ideal $ {y^p}$, Trans. Amer. Math. Soc. 94 (1960), 483-497. MR 22 #4711. MR 0113880 (22:4711)
  • [10] -, A symmetry theorem for the differential ideal $ [uv]$, Proc. Amer. Math. Soc. 12 (1961), 654-657. MR 24 #A115. MR 0130249 (24:A115)
  • [11] -, On a problem of J. F. Ritt, Pacific J. Math. 17 (1966), 149-157. MR 33 #5625. MR 0197460 (33:5625)
  • [12] -, Unusual power products and the ideal $ [{y^2}]$, Proc. Amer. Math. Soc. 17 (1966), 757-758. MR 33 #4053. MR 0195857 (33:4053)
  • [13] 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12H05

Retrieve articles in all journals with MSC: 12H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0321913-9
Keywords: Principal differential ideals, critical weight function
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society