The Jacobian conjecture in two variables

DOI10.1016/0022-4049(85)90099-4zbMath0571.13005OpenAlexW2076018358WikidataQ123362561 ScholiaQ123362561MaRDI QIDQ1061790

Hironori Onishi, Harry Appelgate

Publication date: 1985

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(85)90099-4

zbMATH Keywords

Jacobian conjecture

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials over commutative rings (13B25) Morphisms of commutative rings (13B10)

Related Items (14)

A connection between isochronous Hamiltonian centres and the Jacobian Conjecture ⋮ On the Jacobian conjecture in two variables ⋮ A Note on the Jacobian Condition and Two Points at Infinity ⋮ On Appelgate-Onishi's lemmas ⋮ On the Newton Polygon of a Jacobian Mate ⋮ The Dixmier conjecture and the shape of possible counterexamples. ⋮ On extending Abhyankar's two point lemma to positive weights ⋮ On the two-dimensional Jacobian conjecture: Magnus' formula revisited. I ⋮ On the two-dimensional Jacobian conjecture: Magnus’ formula revisited, III ⋮ On the jacobian equation J(f, g) = 0 for Polynomials in k[x, y] ⋮ Younger Mates and the Jacobian Conjecture ⋮ Polynomial Retracts and the Jacobian Conjecture ⋮ The Jacobian problem as a system of ordinary differential equations ⋮ On the Newton polyhedron of a Jacobian pair

Cites Work

• A generalization of Magnus' theorem
• The amalgamated free product structure of \(\mathrm{GL}_2(k[X_1,\dots ,X_n )\) and the weak Jacobian theorem for two variables]
• On polynomial Solutions of a differential equation
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse

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