Some Remarks on Polynomial Maps. Issue 4 (2nd April 2016) - Yan, Dan; Tang, Guoping
Abstract : In this article, we first discuss the relations among JH r  = 0, JH r −1 · H  = 0, and JH r · x  = 0. Then we give a counterexample to the question mentioned in the Remarks of [3 ] and prove the equivalence among JH ( x (1) ) JH ( x (2) )… JH ( x ( r ) ) = 0, JH ( x (1) ) JH ( x (2) )… JH ( x ( r −1) )· H ( x ( r ) ) = 0, and JH ( x (1) ) JH ( x (2) )… JH ( x ( r ) )· x ( r )  = 0. Finally, we give partial answer to Conjecture 2 in [4 ].