ABOUT THE QUATERNIONIC JCAOBIAN CONJECTURE

In this paper we consider the Jacobian conjecture in the view of hypercomplex analysis. For a polynomial mapping P(w) = (p1(w),p2(w)): ℂ² → ℂ² we discuss the left holomorphic quaternionic function f(z1, z2, z3) = p1 (w) + jp2 (w) where w = (x0 + x1 i, x2 + x3,i) and z1 = x1- x0i, z2 = x2 - x0i, z3 = x3 - x0i. Then we give a new approach to the Jacobian conjecture by the use of argument principle for quaternionic holomorphic functions.