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.

引用

页码：2712 / 2719

页数：8

共 10 条

[1]

Albert A.A., 1957, Mich. Math. J., V4, P1

[2] ELEMENTS OF REDUCED TRACE 0 [J].