AbstractIn this note, we show that, if the Druzkowski mappings F(X)=X+(AX)∗3, i.e. F(X)=(x1+(a11x1+⋯+a1nxn)3,…,xn+(an1x1+⋯+annxn)3), satisfies TrJ((AX)∗3)=0, then rank(A)⩽12(n+δ) where δ is the number of diagonal elements of A which are equal to zero. Furthermore, we show the Jacobian Conjecture is true for the Druzkowski mappings in dimension ⩽9 in the case ∏i=1naii≠0
AbstractIn 1939 Keller conjectured that any polynomial mapping ƒ : Cn → Cn with constant nonvanishin...
Let F = (f,g) : R2 → R2 be a polynomial map such that det(DF(x,y)) is nowhere zero and F(0,0) = (0,...
The Jacobian Conjecture was first formulated by O. Keller in 1939. In the modern form it supposes in...
In this paper, we study a so-called Condition C1 on square matrices with complex coefficients and a ...
AbstractLet k be a field of characteristic zero and F:k3→k3 a polynomial map of the form F=x+H, wher...
Our goal is to settle the following faded problem, The Jacobian Conjecture $(JC_n)$: If $f_1, \cdots...
In 1939 Keller conjectured that any polynomial mapping $f\colon\C^n\to\C^n$ with constant nonvanish...
AbstractIt is proved in [M. de Bondt, A. van den Essen, A reduction of the Jacobian conjecture to th...
We extend a corollary in [2], yielding a sufficient and necessary condition for a polynomial map to ...
In this note we give a short conceptual proof of the Jacobian conjecture in dimension 3 and degree 3...
AbstractWe are concerned with the generalized Jacobian Conjecture which can be reduced to the study ...
Abstract. The paper contains the formulation of the problem and an almost up-to-date survey of some ...
AbstractIn this note we give a short conceptual proof of the Jacobian conjecture in dimension 3 and ...
AbstractLetF≔(F1,…,Fn)∈(C[X1,…,Xn])nwith det(J(F))∈C* and letMi(Xi,Y)=mi0(Y)+mi1(Y)Xi+···+midi(Y)Xid...
AbstractWe show that for all n⩽4 the Jacobian Conjecture holds for all polynomial mappings F:Cn→Cn o...
AbstractIn 1939 Keller conjectured that any polynomial mapping ƒ : Cn → Cn with constant nonvanishin...
Let F = (f,g) : R2 → R2 be a polynomial map such that det(DF(x,y)) is nowhere zero and F(0,0) = (0,...
The Jacobian Conjecture was first formulated by O. Keller in 1939. In the modern form it supposes in...
In this paper, we study a so-called Condition C1 on square matrices with complex coefficients and a ...
AbstractLet k be a field of characteristic zero and F:k3→k3 a polynomial map of the form F=x+H, wher...
Our goal is to settle the following faded problem, The Jacobian Conjecture $(JC_n)$: If $f_1, \cdots...
In 1939 Keller conjectured that any polynomial mapping $f\colon\C^n\to\C^n$ with constant nonvanish...
AbstractIt is proved in [M. de Bondt, A. van den Essen, A reduction of the Jacobian conjecture to th...
We extend a corollary in [2], yielding a sufficient and necessary condition for a polynomial map to ...
In this note we give a short conceptual proof of the Jacobian conjecture in dimension 3 and degree 3...
AbstractWe are concerned with the generalized Jacobian Conjecture which can be reduced to the study ...
Abstract. The paper contains the formulation of the problem and an almost up-to-date survey of some ...
AbstractIn this note we give a short conceptual proof of the Jacobian conjecture in dimension 3 and ...
AbstractLetF≔(F1,…,Fn)∈(C[X1,…,Xn])nwith det(J(F))∈C* and letMi(Xi,Y)=mi0(Y)+mi1(Y)Xi+···+midi(Y)Xid...
AbstractWe show that for all n⩽4 the Jacobian Conjecture holds for all polynomial mappings F:Cn→Cn o...
AbstractIn 1939 Keller conjectured that any polynomial mapping ƒ : Cn → Cn with constant nonvanishin...
Let F = (f,g) : R2 → R2 be a polynomial map such that det(DF(x,y)) is nowhere zero and F(0,0) = (0,...
The Jacobian Conjecture was first formulated by O. Keller in 1939. In the modern form it supposes in...
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