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It is usually admitted, even by the specialists of the Jacobian Conjecture, that it has no hope to be correctly formulated over fields of positive characteristic. This opinion is based on the well… (More)

Let k be a field of characteristic zero and F:kn→kn a polynomial map with det JFϵk∗ and F(0)=0. Using the Euler operator it is shown that if the k-subalgebra of Mn(k[k1,…,xn]) generated by the… (More)

is invertible (with a polynomial inverse). This conjecture is still open for all n 2 2! Many attempts have been made to prove this conjecture and several partial results have been obtained (see the… (More)

The aim of this paper is to introduce a new framework in which the Jacobian conjecture can be studied. In fact, we propose a new much more general conjecture, which we call the Eulerian conjecture.… (More)

Adjamagbo. K. and A. van den Essen, A new inversion formula for a polynomial map in two variables. Journal of Pure and Applied Algebra 76 ( 1991) 119-120. , By computing given. one resultant . the… (More)

Abstract A criterion is given for the invertibility of a polynomial map in two variables over an arbitrary field. A formula for the inverse is derived as wel as other results obtained by McKay and… (More)

The main theorem (Theorem 4.1) of this paper claims that any ring morphism from an Azumaya algebra of constant rank over a com- mutative ring to another one of the same constant rank and over a… (More)

Abstract After the proof of a not very known refinement of the Noether Normalization Theorem, we obtain two sharp degree bounds for the geometric degree of a dominating morphism of irreducible affine… (More)