Note on an elementary proof of a theorem of Nakai and Baba on the Jacobian conjecture in two variables
type: Item
instance of: scholarly article
title: Note on an elementary proof of a theorem of Nakai and Baba on the Jacobian conjecture in two variables
zbMATH Open document ID: 0715.13013
author: Philip P. W. Wong
published in: Southeast Asian Bulletin of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let P, Q be two polynomial-functions in \({\mathbb{C}}[x,y]\). The two- dimensional Jacobian conjecture states that if \(\partial (P,Q)/\partial (x,y)\) is non-zero, then \({\mathbb{C}}[x,y]={\mathbb{C}}[P,Q]\). It has been proved under certain restrictive assumptions concerning the degrees of P and Q. In particular Nakai and Baba have shown that the conjecture is true if the degree of P or Q is 4 or if the larger degree is 2p \((p>2\) being prime). A direct proof by means of elementary computations only is given in this paper.
reviewed by: Gerhard Kowol
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 34M99
zbMATH DE Number: 4177234
zbMATH Keywords: Jacobian conjecture
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4177234