Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A chain rule for multivariable resultants
HTML articles powered by AMS MathViewer

by Charles Ching-an Cheng, James H. McKay and Stuart Sui Sheng Wang PDF
Proc. Amer. Math. Soc. 123 (1995), 1037-1047 Request permission

Abstract:

We present a chain rule for the multivariable resultant, which is similar to the familiar chain rule for the Jacobian matrix. Specifically, given two homogeneous polynomial maps ${K^n} \to {K^n}$ for a commutative ring K, such that their composition is a homogeneous polynomial map, the resultant of the composition is the product of appropriate powers of resultants of the individual maps.
References
    N. Bourbaki, Commutative algebra, Elements of Mathematics, Addison-Wesley, Reading, MA, 1972. F. Faà de Bruno, Théorie des formes binaires, Résumé des leçons faites à l’Université de Turin, Librairie Brero succr. de P. Marietti, Turin, 1876. M. Chardin, Contributions à l’algèbre commutative effective et à la théorie de l’élimination, Thèse de l’Université Pierre et Marie Curie (Paris VI), 1990, preprint of Centre de Mathématiques de l’Ecole Polytechnique F-91128 Palaiseau France. C. C. Cheng, J. H. McKay, and S. S.-S. Wang, Chain rule for multivariable resultants, Abstracts Amer. Math. Soc. 13 (1992), 242 (873-13-109).
  • Arno van den Essen and MichałKwieciński, On the reconstruction of polynomial automorphisms from their face polynomials, J. Pure Appl. Algebra 80 (1992), no. 3, 327–336. MR 1170718, DOI 10.1016/0022-4049(92)90150-E
  • I. M. Gel′fand, A. V. Zelevinskiĭ, and M. M. Kapranov, Discriminants of polynomials in several variables, Funktsional. Anal. i Prilozhen. 24 (1990), no. 1, 1–4 (Russian); English transl., Funct. Anal. Appl. 24 (1990), no. 1, 1–4. MR 1052262, DOI 10.1007/BF01077912
  • N. Kravitsky and Z. Waksman, On some resultant identities, Linear Algebra Appl. 122/123/124 (1989), 3–21. MR 1019980, DOI 10.1016/0024-3795(89)90645-9
  • Ernst Kunz, Introduction to commutative algebra and algebraic geometry, Birkhäuser Boston, Inc., Boston, MA, 1985. Translated from the German by Michael Ackerman; With a preface by David Mumford. MR 789602
    • F. S. Macaulay, Some formulæin elimination, Proc. London Math. Soc. 35 (1903), 3-27. —, The algebraic theory of modular systems, Cambridge Tracts in Math., vol. 19, Cambridge Univ. Press, Cambridge, 1916. J. H. McKay and S. S.-S. Wang, Chain rule for resultant, Abstracts Amer. Math. Soc. 8 (1987), 329 (836-13-122).
  • James H. McKay and Stuart Sui Sheng Wang, A chain rule for the resultant of two polynomials, Arch. Math. (Basel) 53 (1989), no. 4, 347–351. MR 1015998, DOI 10.1007/BF01195214
  • James H. McKay and Stuart Sui Sheng Wang, A chain rule for the resultant of two homogeneous polynomials, Arch. Math. (Basel) 56 (1991), no. 4, 352–361. MR 1094422, DOI 10.1007/BF01198221
  • Patrice Philippon, Critères pour l’indépendance algébrique, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 5–52 (French). MR 876159
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12D10, 13B25
  • Retrieve articles in all journals with MSC: 12D10, 13B25
Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1037-1047
  • MSC: Primary 12D10; Secondary 13B25
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1227515-9
  • MathSciNet review: 1227515