On relations between Jacobians and minimal polynomials

DOI10.1016/0024-3795(93)00220-TzbMath0861.13009WikidataQ126780491 ScholiaQ126780491MaRDI QIDQ1893102

Jie-Tai Yu

Publication date: 20 March 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Gröbner basisJacobiansJacobian conjectureminimal polynomialsinvertible polynomial mapinvertible rational map

Mathematics Subject Classification ID

Birational automorphisms, Cremona group and generalizations (14E07) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10)

Related Items (6)

Remarks on the Jacobian conjecture ⋮ A cancellation conjecture for free associative algebras ⋮ Poisson brackets and two-generated subalgebras of rings of polynomials ⋮ Mappings with a composite part and with a constant Jacobian ⋮ The Preimage of a Coordinate ⋮ Two dimensional coordinate polynomials and dominant maps

Cites Work

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• A resultant criterion and formula for the inversion of a polynomial map in two variables
• Face polynomials and inversion formula
• Reconstructing birational maps from their face functions
• Computing minimal polynomials and the degree of unfaithfulness
• On relations between Jacobians and resultants of polynomials in two variables
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• A criterion to decide if a polynomial map is invertible and to compute the inverse

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