The images of polynomials with zero constant term on strictly upper triangular matrix algebras(常数项为零的多项式在严格上三角矩阵代数上的像)

Abstract

In the present paper, we define the minimum degree of polynomials. By using the minimum degree of polynomials and Zariski topology, we give a complete description of the images of polynomials with zero constant term on strictly upper triangular matrix algebras over an algebraically closed field.(定义了多项式的最小次数。使用多项式的最小次数和Zariski拓扑，给出了代数闭域上常数项为零的多项式在严格上三角矩阵代数上像的完整刻画。)

Keywords

• polynomial(多项式)
• multilinear polynomial(多重线性多项式)
• strictly upper triangular matrix algebra(严格上三角矩阵代数)
• zariski topology(zariski 拓扑)