Test elements, retracts and automorphic orbits

被引：10

作者：

Gong, Sheng-Jun ^{[1
]}

Yu, Jie-Tai ^{[1
]}

机构：

[1] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF ALGEBRA | 2008年 / 320卷 / 07期

关键词：

test element; retract; automorphic orbit; free associative algebra; degree estimate; polynomial algebra; coordinate;

D O I：

10.1016/j.jalgebra.2008.07.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A(2) be a free associative or polynomial algebra of rank two over a field K of characteristic zero. Based on the degree estimate of Makar-Limanov and J.-T. Yu, we prove: (1) An element p is an element of A(2) is a test element if p does not belong to any proper retract of A(2); (2) Every endomorphism preserving the automorphic orbit of a nonconstant element of A(2) is an automorphism. (c) 2008 Elsevier Inc. All rights reserved.

引用

页码：3062 / 3068

页数：7

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