Comment on a Paper by Yucai Su on Jacobian Conjecture (dec 30, 2005)

The said paper [Su2] entitled " Proof Of Two Dimensional Jacobian Conjecture " is false. Comments The Jacobian Conjecture is a well-known hard problem. Recently there are many attempts to solve it. This paper is one of the false attempts. Minor mistakes We have read Su's latest version (Dec 30, 2005) of his papers. There are numerous typos (say, some d ′ s, and all d ′ i s really should be d 2 etc.) and unconventional concepts and notations (say, " rational polynomials (it is a CS notation, not commonly used in Mathematics) " (=rational functions?, or =polynomials with rational numbers as coefficients?) " modulo F(x,y) " means " F[x]((y −1)) as a ring or a commutative group? ". Note that in those two cases, the meaning of " modulo F(x,y) " is totally different.) Those errors should be fixed. Major mistakes One of the mistakes is that on pg 17 of [Su2], let us quote, Lemma 3.10: a'=1. In particular p'=1, q'=d 2 namely, ¯ F 1 (x,y)=y d 2 + c d 2 x for some c d 2 ∈ F *. There are two problems about this lemma which is the kernel of the whole proof in his paper (all previous statements in this paper are largely known in different terminologies) , (1) the proof of the lemma is with gaps, (2) the lemma can not be true since there are counterexamples .