保持粘切的加法满射及其应用

Additive Sujective Maps Preserving Adjacency and Their Application

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 m≥2, Mm（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 Mm,（D）. As applications, the forms of any additive sujective map preserving general linear groups on Mm（D） are given.