Some Remarks on Polynomial Maps. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Yan, Dan; Tang, Guoping
• Is Part Of: Communications in algebra. Volume 44:Issue 4(2016)
• Page Start: 1379
• Page End: 1389
• Publication Date: 2016-04-02
• Subjects: Jacobian conjecture -- Polynomial automorphism -- Semi-elementary; 14R10 -- 14R15; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2015.1027350
• Languages: English
• ISSNs: 0092-7872

Abstract

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 ].