Abstract

This paper introduces a relation between resultant and the Jacobian determinant by generalizing Sakkalis theorem from two polynomials in two variables to the case of (n) polynomials in (n) variables. This leads us to study the results of the type:〖R_i (x_i,u_1,..,u_n )= Res〗_(x_1,…,x_(i-1),x_(i+1),…,x_n ) (f_1-u_1,…,f_n-u_n ) , i=1,..,n ,and use this relation to attack the Jacobian problem. The last section shows our contribution to proving the conjecture.

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The article was added to IASJ on 2022-04-04

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