保持粘切的加法满射及其应用

Abstract

设m 2,Mm(D)是除环D上的所有m阶矩阵构成的加法群.本文应用矩阵几何基本定理刻划了Mm(D)上保持粘切的加法满射.作为应用,还给出了Mm(D)上保持一般线性群的加法满射的形式.

Suppose m2,M_m(D) is the additive group of all matrices of degree m over skew-field D.In this paper,by using the fundamental Theorems of the geometry of matrices we characterize the additive surjective map preserving adjacency on M_m(D).As applications,the forms of any additive sujective map preserving general linear groups on M_m(D) are given.