多重线性多项式在3×3阶上三角矩阵代数上的像

Images of multilinear polynomials on algebra of upper triangular 3 × 3 matrices

借鉴Wang在研究2×2阶上三角矩阵代数上多重线性多项式的像时给出的新方法,给出一个多重线性多项式在3×3阶上三角矩阵代数上像的结构的描述,从而部分回答了Fagundes和Mello猜想,此猜想是著名的Lvov-Kaplansky猜想的一种变化形式.

This study builds on the method developed by Wang for images of multilinear polynomials on algebra of upper triangular 2 × 2 description of the images of multilinear polynomials on algebra of upper triangular 3 × 3 thereby partly solving the Fagundes and Mello conjecture, a variation of the famous Lvov-Kaplansky conjecture.