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A counterexample to a conjecture of Bass, Connell and Wright

Piotr Ossowski (1998)

Colloquium Mathematicae

Let F=X-H: k n k n be a polynomial map with H homogeneous of degree 3 and nilpotent Jacobian matrix J(H). Let G=(G1,...,Gn) be the formal inverse of F. Bass, Connell and Wright proved in [1] that the homogeneous component of G i of degree 2d+1 can be expressed as G i ( d ) = T α ( T ) - 1 σ i ( T ) , where T varies over rooted trees with d vertices, α(T)=CardAut(T) and σ i ( T ) is a polynomial defined by (1) below. The Jacobian Conjecture states that, in our situation, F is an automorphism or, equivalently, G i ( d ) is zero for sufficiently large d....

An algorithm to compute the kernel of a derivation up to a certain degree

Stefan Maubach (2001)

Annales Polonici Mathematici

An algorithm is described which computes generators of the kernel of derivations on k[X₁,...,Xₙ] up to a previously given bound. For w-homogeneous derivations it is shown that if the algorithm computes a generating set for the kernel then this set is minimal.

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