Degree estimate for subalgebras generated by two elements

被引：0
|
作者：
Makar-Limanov, Leonid [1 ]
Yu, Jie-Tai [2 ]
机构：
[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
[2] Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
来源：
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY | 2008年 / 10卷 / 02期
关键词：
degree estimate; two-generated subalgebras; polynomial algebras; free associative algebras; commutators; Jacobians;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We develop a new combinatorial method to deal with a degree estimate for subalgebras generated by two elements in different environments. We obtain a lower bound for the degree of the elements in two-generated subalgebras of a free associative algebra over a field of zero characteristic. We also reproduce a somewhat refined degree estimate of Shestakov and Umirbaev for the polynomial algebra, which plays an essential role in the recent celebrated solution of the Nagata conjecture and the strong Nagata conjecture.
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页码：533 / 541
页数：9
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