Attacking Jacobian Problem Using Resultant Theory

Authors

Alaa Jony, Department of Mathematics-Faculty of Sciences-Damascus University, Syria.Follow
Shawki Al-Rashed, Associate Prof at Arab International University, Acadimic Staff at Department Of Mathematics, Faculty of Science, Damascus University of SyriaFollow

Abstract

This paper introduces a relation between resultant and the Jacobian determinant by generalizing Sakkalis theoremfrom two polynomials in two variables to the case of (n) polynomials in (n) variables.This leads us to study the results of the type:�Ri���(�xi���,u1,..,un)=Res�x1,...,xi-1,x+1,...xn�(f1−u1,...,fn−un),��i=1,..,n,and use this relation to taatcathe Jacobian problem. The last section shows our contribution to proving the conjecture

Keywords

Jacobian conjecture, polynomial map, resultant.

Article Type

Article

How to Cite this Article

Jony, Alaa and Al-Rashed, Shawki (2022) "Attacking Jacobian Problem Using Resultant Theory," Baghdad Science Journal: Vol. 19: Iss. 2, Article 16.
DOI: https://doi.org/10.21123/bsj.2022.19.2.0336