三变量中的一类坐标多项式

数学季刊 ›› 2006, Vol. 21 ›› Issue (4): 482-487.

三变量中的一类坐标多项式

Department of Mathematics University of Science and Technology of China,Department of Mathematics,University of Science and Technology of China,,Hefei 230026,China,Hefei 230026,China

收稿日期:2004-12-27 出版日期:2006-12-30 发布日期:2023-11-17
作者简介:GONG Sheng-jun(1980-),male,native of Qichun,Hubei,a master student of USTC,engages in algebra and affine algebraic geometry;LI Shang-zhi(1947-),male,native of Neijiang,Sichuan,a professor of USTC,one of the earliest Ph.D.receivers in China,engages in algebra and group theory.
基金资助:
Supported by the NNSF of China(10071078)；

Some Coordinate Polynomials in Three Variables

Department of Mathematics University of Science and Technology of China,Department of Mathematics,University of Science and Technology of China,,Hefei 230026,China,Hefei 230026,China

Received:2004-12-27 Online:2006-12-30 Published:2023-11-17
About author:GONG Sheng-jun(1980-),male,native of Qichun,Hubei,a master student of USTC,engages in algebra and affine algebraic geometry;LI Shang-zhi(1947-),male,native of Neijiang,Sichuan,a professor of USTC,one of the earliest Ph.D.receivers in China,engages in algebra and group theory.
Supported by:
Supported by the NNSF of China(10071078)；

摘要/Abstract

摘要： In this paper,we introduce a polynomial sequence in K[x],in which two neigh- bor polynomials satisfy a wonderful property.Using that,we give partial answer of an open problem: if φ(x,y,z)=(f(x,y),g(x,y,z),z),which sends every linear coordinate to a coor-dinate,thenφis an automorphism of K[x,y,z].As a byproduct,we give an easy proof of the welt-known Jung’s Theorem.

关键词: coordinate polynomials, Jacobian Conjecture, polynomial automorphism, tame
automorphism, algebraically closed field

Abstract: In this paper,we introduce a polynomial sequence in K[x],in which two neigh- bor polynomials satisfy a wonderful property.Using that,we give partial answer of an open problem: if φ(x,y,z)=(f(x,y),g(x,y,z),z),which sends every linear coordinate to a coor-dinate,thenφis an automorphism of K[x,y,z].As a byproduct,we give an easy proof of the welt-known Jung’s Theorem.

Key words: coordinate polynomials, Jacobian Conjecture, polynomial automorphism, tame
automorphism, algebraically closed field

中图分类号:

O174.14

龚胜军, 李尚志. 三变量中的一类坐标多项式[J]. 数学季刊, 2006, 21(4): 482-487.

GONG Sheng-jun, LI Shang-zhi. Some Coordinate Polynomials in Three Variables [J]. Chinese Quarterly Journal of Mathematics, 2006, 21(4): 482-487.

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