一类矩阵代数的多项式恒等式

POLYNOMIAL IDENTITIES FOR A KIND OF MATRICES

本文研究域F上的形如:的n阶方阵构成的矩阵代数R_n的多项式恒等式,主要结论是:xy-yx是R_n的中心多项式;(xy-yx)~2是R_n的恒等式;R_n的最低次恒等式的次数是3.

In this paper, a kind of matrics Rn is studied, the matrices of Rn have the form: Our key aid is researchnig polynomial identities of Rn. We obtain the follauing results: [x,y] is a central polynomial of Rn, [[x,y],z] is an identity of Rn and the minimal identity of Rn. Hence the degree of the minimal identities of Rn is 3.