On the Jacobian conjecture: Reduction of coefficients
type: Item
instance of: scholarly article
title: On the Jacobian conjecture: Reduction of coefficients
zbMATH Open document ID: 0816.13017
author: Jie-Tai Yu
published in: Journal of Algebra
publication date: 1995-03-20T00:00:00Z
review text: The author proves the following two particular cases of the jacobian conjecture: I. Let \(F : \mathbb{R}^ n \to \mathbb{R}^ n\) be a real polynomial map of the form \(F(X) = X - N(X)\), \(X = (X_ 1, \dots, X_ n)\), \(N\) contains no linear and constant terms and coefficients of \(N\) are nonnegative. If the jacobian of \(F\) is a nonzero constant, then \(F\) is an automorphism (even more, \(F\) is a stable tame automorphism). II. If the above theorem holds for every \(n\) and every \(F\) (of the above form) with non-positive coefficients, then the jacobian conjecture is true for all \(n\) and all fields of characteristic zero.
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14H37
Mathematics Subject Classification ID: 12D10
zbMATH DE Number: 735313
zbMATH Keywords: jacobian conjecture
zbMATH Keywords: real polynomial map
zbMATH Keywords: tame automorphism
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
full work available at URL: jabr.1995.1024
OpenAlex ID: W1995951098
Wikidata QID: Q123122034
DOI: 10.1006/JABR.1995.1024
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description: scientific article; zbMATH DE number 735313