A criterion to decide if a polynomial map is invertible and to compute the inverse

DOI10.1080/00927879008824067zbMath0718.13008OpenAlexW2060832716MaRDI QIDQ5749394

A. R. P. van den Essen

Publication date: 1990

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879008824067

zbMATH Keywords

Gröbner basesJacobian conjecturepolynomial idealspolynomial mapping

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials over commutative rings (13B25) Automorphisms of curves (14H37)

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Computing minimal polynomials and the inverse via gcp, Locally nilpotent derivations and their applications. III, On relations between Jacobians and minimal polynomials, A Gröbner basis criterion for birational equivalence of affine varieties, A resultant criterion and formula for the inversion of a polynomial map in two variables, A Gröbner basis criterion for isomorphisms of algebraic varieties, On modules with finite uniform and Krull dimension, A resultant criterion and formula for the inversion of a rational map in two variables, On the reconstruction of polynomial automorphisms from their face polynomials, Automorphisms from face polynomials via two Gröbner bases, On a problem about face polynomials, On the Jacobian conjecture: A new approach via Gröbner bases, On topological approaches to the Jacobian conjecture in ℂⁿ, A counterexample to Meisters' cubic-linear linearization conjecture, Gröbner bases and the Nagata automorphism, Computing minimal polynomials and the degree of unfaithfulness, Tame and Wild Coordinates of 𝐾[𝑧[𝑥,𝑦]]

Cites Work

• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse