# Jacobian conjecture

Known as: Jacobian problem, Keller's problem, Smale's sixteenth problemÂ
In mathematics, the Jacobian conjecture is a celebrated problem on polynomials in several variables. It was first posed in 1939 by Ott-Heinrichâ€¦Â (More)
Wikipedia

## Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2009
2009
The Jacobian Conjecture is the following : If Ï† âˆˆ Endk(Ank ) with a field k of characteristic zero is unramified, then Ï† is anâ€¦Â (More)
Is this relevant?
2008
2008
A non-zero constant Jacobian polynomial map F = (P, Q) : C â†’ C has a polynomial inverse if the component P is a simple polynomialâ€¦Â (More)
Is this relevant?
2004
2004
The Jacobian Conjecture can be generalized and is established : Let S be a polynomial ring over a field of characteristic zero inâ€¦Â (More)
Is this relevant?
2004
2004
Let z = (z1, Â· Â· Â· , zn) and let âˆ† = âˆ‘n i=1 âˆ‚2 âˆ‚z2 i be the Laplace operator. The main goal of the paper is to show that the wellâ€¦Â (More)
Is this relevant?
2004
2004
• Ludwik M. DruÅ¼kowski
• 2004
It is sufficient to consider in the Jacobian Conjecture (for every n > 1) only polynomial mappings of cubic linear form F (x) = xâ€¦Â (More)
Is this relevant?
2004
2004
Let K[x, y] be the algebra of two-variable polynomials over a field K. A polynomial p = p(x, y) is called a test polynomial forâ€¦Â (More)
Is this relevant?
2001
2001
New combinatorial properties of Catalan trees are established and used to prove a number of algebraic results related to theâ€¦Â (More)
Is this relevant?
Review
2000
Review
2000
In this paper we give an update survey of the most important results concerning the Jacobian conjecture: several equivalentâ€¦Â (More)
Is this relevant?
1998
1998
We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of aâ€¦Â (More)
Is this relevant?
Highly Cited
1982
Highly Cited
1982
Introduction I. The Jacobian Conjecture 1. Statement of the Jacobian Problem; first observations 2. Some history of the Jacobianâ€¦Â (More)
Is this relevant?