Some relations in the polynomial rings associated with polynomial mappings of the plane (part 2)

This article presents a proof of a theorem that was formulated in paper [4]. In addition, new relations are obtained for some polynomials in n variables over the field of complex numbers. These polynomials are related to polynomial mapping of the plane with a constant Jacobian. As is known, the question of the invertibiliti of a polynomial mapping F with a constant Jacobian det J(F) was formulated by Keller O.H. in 1939. Based on the properties of these polynomials, a necessary and sufficient condition for the constancy of the det J(F) in the two - dimensional case is obtained.