On multilinear polynomials in four variables evaluated on matrices

被引：18
|
作者：
Buzinski, David [1 ]
Winstanley, Robin [2 ]
机构：
[1] Case Western Reserve Univ, Cleveland, OH 44106 USA
[2] Univ Washington, Seattle, WA 98195 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2013年 / 439卷 / 09期
基金：
美国国家科学基金会;
关键词：
Multi linear polynomial; Trace; Matrix algebra;
D O I：
10.1016/j.laa.2013.08.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let K be an algebraically closed field of characteristic 0 and let M-n(K), n >= 3, be the matrix ring over K. We will show that the image of any multilinear polynomial in four variables evaluated on M-n(K) contains all matrices of trace 0. (C) 2013 Elsevier Inc. All rights reserved.
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页码：2712 / 2719
页数：8
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