Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Younger mates and the Jacobian conjecture

Authors: Charles Ching-an Cheng, James H. McKay and Stuart Sui Sheng Wang
Journal: Proc. Amer. Math. Soc. 123 (1995), 2939-2947
MSC: Primary 14E09; Secondary 13B25
MathSciNet review: 1257100
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ F,G \in \mathbb{C}[x,y]$. If the Jacobian determinant of F and G is 1, then G is said to be a Jacobian mate of F. If, in addition, G has degree less than that of F, then G is said to be a younger mate of F. In this paper, a necessary and sufficient condition is given for a polynomial to have a younger mate. This also gives rise to a formula for the younger mate if it exists. Furthermore, a conjecture concerning the existence of a younger mate is shown to be equivalent to the Jacobian conjecture.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14E09, 13B25

Retrieve articles in all journals with MSC: 14E09, 13B25

Additional Information

PII: S 0002-9939(1995)1257100-4
Keywords: Jacobian conjecture, Jacobian hypothesis, Jacobian mate, younger mate, automorphism, automorphism pair, Sylvester matrix, resultant, Newton polygon
Article copyright: © Copyright 1995 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia