Non-zero constant Jacobian polynomial maps of $ℂ²$

A ug 2 00 4 Two remarks on non - zero constant Jacobian polynomial map of lC 2 ∗ Nguyen

We present some estimations on geometry of the exceptional value sets of non-zero constant Jacobian polynomial maps of l C and it’s components. 2000 Mathematical Subject Classification: 14 H07, 14R15.

Polynomial maps with strongly nilpotent Jacobian matrix and the Jacobian Conjecture

On strongly Jordan zero-product preserving maps

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

Inversion of polynomial species and jacobian conjecture

We consider the following problem in the theory of (virtual) species of structures: Given a polynomial species F such that its derivative dF equals 1, will its inverse w.r.t substitution F h?1i also be polynomial species? We shall see that this is in general not the case. From this result it follows that an analogue of the jacobian conjecture in the context of species does not hold.

Endomorphisms of Polynomial Rings ; the Jacobian Conjecture

The Jacobian Conjecture is established : If f1, · · · , fn be elements in a polynomial ring k[X1, · · · , Xn] over a field k of characteristic zero such that det(∂fi/∂Xj) is a nonzero constant, then k[f1, · · · , fn] = k[X1, · · · , Xn]. Let k be an algebraically closed field, let k be an affine space of dimension n over k and let f : k −→ k be a morphism of algebraic varieties. Then f is given...