A note on a note by Mutsuo Oka (Q2479934)

To prove the Jacobian conjecture in two variables, \textit{M. Oka} [Acta Math. Vietnam. 32, 125--140 (2007; Zbl 1141.14042)] suggests to show that there is no polynomial which satisfies certain four necessary conditions. In the present paper the author, mixing Oka's strategy with that of \textit{S. Kaliman} [Proc. Am. Math. Soc. 117, No. 1, 45--51 (1993; Zbl 0782.13017)], proves indeed the existence (and presents examples) of polynomials satisfying all the conditions of Oka's Theorem.